Strips are notoriously inaccurate, and I usually don't belive them, but
with such small waterchanges and a heavy stocking, I'd say 250ppm is in the right ball park
The fact that the new fish only went over and the tank is heavily stocked only reciving small waterchanges at this point makes me suspect that you are dealing with OTS (Old Tank Symdrome) where a build-up of various toxins has occured. The established fish grow used to this and don't get harmed. New fish however won't be used to it, and will struggle at best, or even die. Symptoms for OTS are quite varied and none-specific and can include, but are not restricted to;
loss of weight
Burns on the body, similar to those associated with ammonia burns e.t.c
Loss of "ballence""
Gasping
Loss of apetite
loss of colour
There are others, that don't imediately spring to mind. Not all affected fish will show all symptoms, and the symptoms displayed can be very none-specific.
Do a test with Liquid drop test kits so you have some accurate readings and post back.
In the mean time got into some small, say 5-10%, daily waterchanges to try to dilute down the toxins. Don't do large waterchanges, as toxic shock (that I suspect killed the new fish as a result of OTS) can work both ways. Suddenly decreasing the toxin levels in the tank can do the same as introducing fish to ususually high toxin levels.
Recovering a tank from OTS requires a "slow but steady wins the race" approach. After a week start waterchanges that are twice as large as in the first week and start reviewing the readings. Once nitrate has dropped back to a reasonable level, go onto weekly 30-50% waterchanges and wait a month before thinking about more fish
Nitrate wants to be no higher than 50ppm above that of your tap water. If it is higher, you either aren't waterchanging often enough (not true here, weekly should be fine), or you aren't changing enough (the problem here IMO)
All the best
Rabbut