I'm certainly not doubting that your creatures died and/or that your shrimp look sick. I never questioned that.
I can readily accept that elevated nitrate levels may make some inverts listless and not look right. That happens for most chemicals at levels well below where they cause death.
And while I still do not have a good understanding of what the nitrate levels were, they certainly may have been higher than people normally recommend. Remember too that test kits are frequently inaccurate (for many reasons) and some nitrate kits have issues (or at least have in the past, they change so often it is hard to say for any given kit). It does not mean you are stupid if you use a kit and get a wrong answer. Nearly every week there are test kit errors discussed in this forum that are causing folks stress.
So one important question is whether the nitrate is what did the killing, primarily because if you fix it and the tank still doesn't thrive, you'll still have a problem.
One thing to bear in mind is that there is an endless stream of folks who lose inverts for reasons they cannot identify (or have not yet identified). There are many reasons they can die, and many of them involve things you have not tested for. So having a high nitrate measurement at the time of death does not prove the nitrate killed them.
So the cause and effect of the nitrate and the deaths is an open question, IMO. In fact, I think it equally likely that the deaths contributed to the elevated nitrate rather than the nitrate causing the deaths, although both may be true.
So I will just repeat that it is possible that you lost some inverts to nitrate, but it isn't apparent to me that nitrate is the primary explanation.
So here are my suggestions...
1. If you think the nitrate level is rising fast, then there must be some big source(s) of ammonia in the tank from decaying foods, dead organisms, etc. That does not mean that ammonia is elevated, but it might be despite a measurement that suggests it is not (possible test kit errors again, or maybe it spiked and dropped again before you took a measurement, etc.). Ammonia is far, far more toxic than is nitrate, and there are clearly known bad effects of ammonia at levels below where it kills organisms. If the level has risen above 0.1 ppm, I generally suggest taking action.
So if nitrate continues to rise rapidly (say, more than 2 ppm per day), I'd consider treating the tank with something to reduce the toxicity of the ammonia, such as Seachem Prime or Amquel and see if it seems to have any apparent effect on organism appearance after a few days of treatment.
2. I'd look carefully for potential dead organisms and remove them. If it seems the live rock has dead organic tissue on it, that might require the rock to be removed and bleached or otherwise treated to remove this organic matter.
3. I'd make sure you are not overfeeding the tank.
4. Are you using tap water? Are there any metal parts in the system, or that are exposed to any thing entering the tank (like top off water)? The concern here is primarily copper but other metals can also cause the invert effects you are seeing. Running a Boyd Polyfilter or Seachem Cuprisorb or Two Little Fishies Metasorb might be a prudent action to take and won't hurt if metals are not the problem.
5. Continue water changes if nitrate is above about 10 ppm.
6. Relying on the LFS for water might not be best if you do not know how they are making it or how pure it is.
After these immediate actions, I'd look to long term nitrate control. There are many methods, including growing macroalgae, organic carbon dosing, denitrators of various sorts, replacing the canister filter, etc.
And a few questions to try to understand better...
1. Are there any inverts thriving in the tank?
2. Were they all obtained from the same source?
3. How long has the tank been set up?
4. What kits are you using for nitrate and ammonia?