ADA shower in too small bathroom

My apologies for not having a nice drawing program but I will attach a rough sketch and hope it is understandable... I'm mainly just asking for thoughts & ideas.
Really need help with this one. I'm supposed to be putting in an ADA compliant shower in a bathroom which has a toilet & vanity. Vanity is roughly 30" left to right tho' I'm not sure about front to back so let's just guess at 24". The overall wall to wall dimensions of the bathroom is 67" wide x 84". This is a government grant deal so I can not vary from their stipulations. From my best guestimations there's no way to put in a shower with minimum inside dimensions of 36" x 36" and still have room for a toilet and 36" x 48" space in front of the shower along with the existing vanity. The entry door is 32" on the 67" end.
Any help with this, advice, etc. would be greatly appreciated. I had planned on just buying a cheap shower kit with a seat in it but I just noticed the spec's call for it to be ADA compliant. Now I'm toying with the idea of going with tile if I can figure out how to make it work and exactly what is required to be ADA. I've done these jobs before but never run into this issue of not enough room to put everything in. How can that be dealt with? Will there be allowances for "pre-existing" conditions? Other than RUN... what would you do to get the job and satisfy the requirements?
As you can imagine this job is in a VERY old house in a very old low income community.

You CANNOT have an ADA compliant room with a 32" door and less than a 36" passage between the sink and shower wall. What good would an ADA shower be if "ADA people" cannot get to it? IT would be difficult for "non handicapped" people to get through a 12" opening. Usually there are NO allowances for existing conditions. You are expected to change things to meet the requirements.

Chuck the vanity, make the whole room a wet room so you do not need any shower door or walls. Use a wall-hung sink or counter so a wheel-chair can access it. There are some very specific wheel-chair turning spaces required to comply with ADA bathroms. If you get a chance, see if you can visit one of the newer rehab facilities...they tend to use this sort of technique. The entire room gets tiled and waterproofed as if it was a shower, including the toilet area and sink.

hj.. I totally respect everything you said in your post and totally agree... but all I have to worry about is what is spec'd in the contract. Modifying the door or replacing or moving the vanity/sink is not on the list of things to do. Spec's do not call for a complete ADA compliant bathroom.... doesn't make sense but that's the contract.
BTW... the door and vanity project can be added to the next grant this home owner gets...

Jim, if I recall correctly the wheel chair turning area for a transfer type shower are 36" x 48". With a 36"x36" (inside dimensions) shower, 40" x 40" outside dimensions this would leave less than 48" in front of the shower. Too the wall between the shower and toilet would be too close to the toilet. In my opinion the whole project is impossible to satisfy ADA or any other code requirements... this project may be one that I should run from...