It is not likely an acclimation procedure I would bet. E especially since there should be virtually no ammonia built up in bags of fish brought home from a local store, they were not bagged long enough for that. Most acclimation is useless anyway since a fish will not actually acclimate to major differences in much less than one to two weeks. And if they are out of their safe temp range and in danger from this, the solution it to get them back into proper temps ASAP.
I doubt it has anything to do with nitrate. If it was so high in your tanks to be the cause, some of your existing fish would likely be in trouble as well.
This really leaves a few reasonable things to consider. Though I doubt it was aggression between existing and new fish, it would help to know what these are to help rule this out 100%. But, I would think if the fish were fighting seriously, either you would have noticed this and/or there would have been some injuries on some of your other fish.
The real question is whether the cause of the deaths is due to something in your tanks or is it due to your getting fish in "bad" shape. If things were off in your tanks, the odds are it would also eafect the fish you already have in them. On the other hand, the fish which died all came from one place, so I think it pays to look at this side of things.
Since the fish were varied I would assume they were all not in the same tank in the store. So the questions that come to mind here are:
1. How did the fish look generally in the store tanks? Did you see any dead or apparently sick fish in any of them, specially the ones from which your new fish came?
2. Do you know if the store has a central filtration system or has tanks ganged on a few common systems? Many stores do.
3. Do you know how long the store had the fish before you bought them?
4. What have your past experiences been when purchasing form this store?
5. How did the dead fish behave in your tanks before they died? Did they hide? Did they eat? Did they behave oddly in any way?
6. Did the fish show any symptom, either physical or behavioral, between the time you got them and the time they died?
6. Did you call or visit the store since the fish died and discuss this with them? If so, what did they have to say?
When you say parameters were off, I assume you mean relative to those at the store. If this is not the case then what did you mean and then do you know the store tank params in the tank or tanks out of which your new fish came?
When I see over 50% of fish die within a relatively short period, I normally assume it is related to a common cause. Because you are not losing any of your existing fish, my instinct is to look to the store as the source of the problem and not your tanks.
Diagnosing fish for most things is extremely difficult for us as hobbyists. If it is not something clear cut such as Camallanus worms or Ich, the actual root cause may be invoisible to us. Combine that with trying to do remote diagnosis and the problems are magnified. Unfortunately, there are not many fish vets. So we are forced to do the best we can with what we have.