Tank Transfer Method doesn't help with velvet, and that's probably the most likely disease for you to encounter right now.
As far as ditching your LFS, I say no. You should just lower your expectations of ANY LFS. There really isn't much they can do about fish disease that makes economical sense. Sure they could prophylactic QT everything, but that would be very expensive and drive the price of their fish up. The vast majority of their customers probably would just think they were overpriced and buy from their competitors.
As far as whether or not to QT, i've bought about 30 fish in the last two years, stocking my own tank and that of my nephew. Most of my purchases were from Live Aquaria and Divers' Den, which probably have better disease prevention protocols than most local fish stores, but about 60% of the fish have displayed disease symptoms within the first couple of days after I received them. That has been true of both LFS and online purchases. The one exception has been online purchases of ORA captive bred fish purchased at LA, which seem to come directly from ORA in FL (and possibly skipping the normal distribution chain). That could also be a coincidence, so I don't take chances. To me, all this simply means the responsibility for clearing the fish of diseases falls on me. It's a bummer, because there's definitely a learning curve, but it's not all that inconvenient once you get the hang of it.
To me the super important things are:
1) seed filter media with bio-spira so you don't have to worry about ammonia.
2) get the salinity in your QT to match the water your fish will come in so acclimation is easy
3) use chelated copper like copper power for 2 weeks after bringing it up to theraputic levels over 2 to 4 days depending on sensitivity of the species (using a hanna checker to measure) - this makes copper easy and covers the most likely and probably most disasterous disease, velvet (bonus, it also covers ich)
4) transfer to a clean tank and administer general cure twice a week apart (covers flukes which are super common and uronema which is also pretty common in some species)
5) be ready to administer the trifecta or NFG if a bacterial infection pops up (this happens to me a lot with wrasses and anthias, others have reported it's common with angels)
6) have either Ruby Reef Rally or a formalin product on hand in case of emergency
7) also have a specimen container on hand in case you need to do a freshwater dip (which I end up doing often to rule out flukes)
This is going to cover you for the vast majority of what you're likely to encounter. The other things, like focus + metro for internal parasites don't kill as fast, so you can acquire meds as they pop up usually.
You can do all this with the 10g setup
@Dom described above. It isn't cheap, but it is relatively easy, particularly after you've done it once or twice.
