Hi Wideawake,
If you are only considering manufacturers or retailers in the NYC area then post #2 here includes the better options and possibilities I’m aware of in the area (although there are many online options outside of the NYC area that would also be well worth talking to that also have good return or exchange policies if you are open to a non NYC online purchase).
While your budget is on the low side for latex … the posts I linked in my last reply that list some of the lower budget latex options I’m aware of do have a few options that would be in your budget range.
Casper is an “all or nothing” choice and would certainly be a better quality/value option than most of the mainstream choices that would be available to you and because they have a good return policy … if it doesn’t turn out to be a suitable choice for your parents based on their sleeping experience then there is little risk involved in trying them although only a twin (not a twin XL) would be in your budget range and this may be a little bit on the short side for your dad (he is only 5" shorter than the mattress).
If you follow the steps in the tutorial one at a time (without missing any) and narrow down your options with each of the retailers or manufacturers you are considering to a single mattress then it will be much easier to make a final choice between your finalists.
Phoenix