Dunno alot about auto tranies but i've messed around w/ the TH350 and read a bunch about the 200 and 700R's before I decided on a manual for my Z. So I'll throw a coupld of things out there.
The TH350 has a vacum line to the valve body if you disconnect and PLUG it, it will change the VB to full manual, I'm pretty sure. (your 700R has one right or is it electronic?) So, if you remove the vacume or electric signal to the trans telling it when to shift, and disconnect the kick-down cable from the carb linkage, you should be able to shift it manually 1-2-3-OD and vice versa.
If you can shift manually, then your issue is in the adustment of the Kickdown or TV (always trying to kick down?) or the vacume / electric signal to the VB.
If you can't shift manually then the issue is probably in the tranny.
Keep checking the fluid for burning and low level, check it cold and hot untill you are POSITIVE there is enough in there.
EDIT: OH!!! and are you SURE you have the correct shifter and have it adjusted correctly? I can't imagine how you would not have Neutral unless the linkage is not adjusted correctly. It's esay to get the wrong hardware w/ an aftermarket "one size fits all" type shifter.