2001 P71 trans time

I understand I need the '70' trans not the '75' what I would like to know is what else I can get one from. I found one for sale in Jersey (I live in central NY) that belonged to a GT and I'm not sure how to tell if it would fit. Let me try to organize my thoughts...

What fits for an 01?

Best voted option for how to go about replacing it? I'm not doing it myself, to be clear. What I mean is, used trans (they seem hard to find) AAMCO center, independent shop rebuild, Ford themselves, or order a rebuilt one from a company I'll post a link to below. All I really want is the cheapest option, but I also don't want future problems (crappy rebuild) which is obvious but I said it anyways.

All forward gears are gone. The previous owner went off the road, got stuck in a ditch, and just kept putting it to the floor until someone realized the wheels were no longer spinning. Toasted right? I just assumed it's new trans time due to that stupidity. (he still does this to every car he gets stuck...guess there's a lot of free cars in my future)

http://www.monstertransmission.com/Transmissions--Mild_c_7744.html

You need a trans with the long tailshaft for a direct swap, this includes the P71 and the Town Car for a direct swap. The same year would be the best option since there were often changes made between years to make things a little difficult.
I would recommend going to a local shop for a rebuild, this way any warranty issues are dealt with in person and should only take a day or 2 to get sorted. If you were to get something from an online retailer like Monster, if it fails they need to have it back to cover the warranty, this means taking it out and sending it back to them...I doubt any install costs or shipping costs are covered and who knows how long it takes.

Excellent point.
I suppose then my first stop will be Sure Shift transmissions in Newfield NY.

Thank you for the detailed info. May be able to find a Town Car around but I like the thought of a warranty if I'm spending several hundred anyways.

What are people paying for a rebuild? I've read things online claiming as low as 1200 but then my dad's '04 Explorer trans was at least 2200 for AAMCO to rebuild (which apparently wasn't an AAMCO shop starting that year but they had been) perhaps that was because it was 4x4?

Something I forgot to ad (mostly since I realized it today) the car does 'engage' in some form when a forward gear is selected. By that I mean the idle drops as if it were in gear. The drive shaft does not spin. I checked this just in case it was a broken axle or something that would allow reverse to still function other than a trans issue.

UPDATE

Car is back in motion. Got it back in 3 days time. $900 for forward motion. It was the forward clutches that were toasted. Nice to find a shop that won't just tell you you need a whole new unit (which is why my friend lost interest in the vehicle).