I've been thinking things over today and it dawned on me that it might work better to use the 20 gallon tank for placing the live ocean rock in to grow the biofilm on the other rocks and keep the stars in smaller tanks (1 to a tank). That way the stars wouldn't have to be removed and transferred for feeding and it would solve the problem of the stars getting uneven nutrition in the holding tank. I think to ensure that the stars are getting an even amount of biofilm, the rocks should be close in weight. (That would answer the question asked by the expert regarding making sure they have access to the same amount of food.) Does it matter if the small tanks with the stars are slightly different sizes though? I don't think it does since the food will be transferred to the tanks (5 gallon vs 8 gallon or something like that). Also, since part of the purpose of the experiment is to enable us to better keep them in home aquariums, should I also give equal rations of a supplemental food source such as oysters or maybe Masstick to each star? I find it hard to believe that the biofilm will generate quickly enough to avoid starvation (although they are known to last months in small inadequate tanks so maybe that's not as much of an issue.) After all, progress will be tracked by weight.
The key with studies like this is to get and keep everything as close to the same as possible. So, here's how I would personally do it:
1 ) Stars are all kept in bare-bottom or dry-sand tanks with a shared sump/refugium (as you and Timfish suggested above) and target fed with pieces of the same food of the same weight (oysters or Masstick would both work as long as you know the stars will eat them):
These steps would eliminate issues with water quality difference between the starfish holding tanks that could be confounding variables, and they would eliminate differences in diet which could be confounding variables.
2 ) Different biofilms (as confirmed by microscope observation) are grown out in different little tanks (weighing the media [likely dry rock or something like ceramic disks] - which should be as close in size and shape and weight as you can get each piece of media to be - it is grown on in advance and weighing the media it is grown on after the biofilm has colonized it, and offering pieces which have shown similar increases in weight - the weight difference will likely be tiny, so you would need a very sensitive scale for this) and offered two at a time to a single, three-day starved, sea star in a third tank at equal distances from the star. Once the star is done feeding, I would weigh both pieces of offered media again to try and gauge how much they ate (they would be placed in the feed preference test tank for a set amount of time and removed when that time is complete - the COTS study I've read used 48 hours as the time in the test tank, so, it would depend on the initial size of the stars and the size of the media pieces used to offer food to them, but I'd probably use that timeframe too if the pieces are relatively close in size to the stars, and I would assume that the piece they go for first is their preferred film unless they ate substantially more weight wise on the other piece) :
While not perfect, this would offer a reasonable level of control to the feeding and a reasonable level of assurance that the feeds offered are of similar value (from the experimenter's perspective, not necessarily the sea star's). Additionally, by using media similar to the rock which the biofilm is originally grown on - such as dry rock or a ceramic media - you should be able to avoid issues with the biofilm having a different preferred media for growth (some prefer/grow better on rocks, some sand, some glass, some metal, some plastic, etc. - so keeping the media of a similar composition reduces the likelihood of a change in biofilm composition from rock to media).
3 ) I would weigh (I don't know if wet weight or dry weight would be better, so I'm inclined to say I would use both wet and dry as Timfish suggested above to be safe) and measure the starfish (arm length and disc diameter) at the start of the study and probably on the first day of starving every time they are starved before a feed preference test (ideally, all the stars would either be starved at the same time and preference tested the same day, or they would be tracked individually and share the same testing schedule as the others - i.e. they would all go x days being fed as normal, then starved for three days, then preference tested):
Consistency with testing like the measuring and weighing is key to good data. Record everything you can.
4 ) Once a preferred biofilm has been found using the feed preference testing, I would consider experiment number one complete, and I would begin experiment number two. Experiment number two would be run pretty much the exact same as experiment number one, but it would be using exclusively the same biofilm feed at different ages in the preference testing (i.e. I would use biofilm x at two weeks of media colonization and four weeks of colonization as the food options for the preference test - find out which is preferred of those two and then test it against biofilm x at six weeks of colonization) :
Figuring out a preferred film first and a preferred film age second would greatly simplify the testing process, but you could include different ages of films in the first experiment to see if that influences the stars' preferred film choice.
5 ) Once a preferred film age has been determined, I would consider experiment two complete, and I would move on to experiment three - determining how much of their preferred biofilm they eat on average daily as determined by weight of media offered before and after feeding. Carried out with a similar starvation then feeding method (definitely only using one star at a time for this experiment), I would starve the star for three days, then put it in the feeding experiment tank with several pieces of their preferred biofilm media (the goal would be to add more than they could realistically eat so that you can compare the before and after weight difference of the offered media at the end of the 48 or whatever hour long time period they're in the tank for and get an idea of how much they eat by weight) :
Because you'd be weighing each piece of media offered to the star before and after each feeding, you may have some idea by this point of how much they'll eat in a set amount of time - this would be trying to confirm that. There would be some error, as the biofilm could start recolonizing the cleared media in that 48 hour timeframe, but it would get you into the ballpark of how much they eat. I assume this would give a relatively accurate measure of feed consumed, but I may well be wrong - if the expert you're in contact with has better suggestions, I would love to hear them.
6 ) From here, I would be done with the starvation and feeding experiments, and I would try to figure out ways to produce enough of the preferred feed for the stars (using the starvation levels of eating as an estimated ceiling for how much they may consume daily). I would change from feeding the stars the oysters or Masstick to trying to feed them their preferred biofilm. Importantly, I would still track the weight of media offered before and after feeding to see if the stars eat less when not starved.
That's how I would do this experiment. Now, to address some other points above, you are correct that you likely wouldn't be able to produce enough biofilm feed to keep all of the stars from starving, so you may want to give some away after the tests are complete. The goal, however, would be to figure out what they prefer quickly enough that you could figure out how (if possible) to grow it in sufficient quantity to prevent their starvation. Also, until step 5, I would assume the amount of biofilm offered would be limited for feeding.