727 problems, opinions wanted...

The guys are correct about it being a classic case of torque converter drain back which torqueflites are famous for. Also correct is the part about putting it in neutral for a few seconds before you put it in drive to fill the converter.

Wanting to pull when in neutral could be a product of the last person that rebuilt it set the rear clutch pack tolerances a little too tight. Or it could be a valve body problem. The only way to tell for sure is to check the pressure going to the clutch pack when in neutral. If it has any pressure it's a valve body problem. If it don't have pressure it's a clutch pack problem.

I would also recommend what Duster440 said and pull the pump out for inspection of the bushing and replace it if needed and replace all the pump seals. The only thing I can add to this is if when you pull the pump out the clutch packs will also want to fall out because the front pump is basically what holds them in place. If you tighten the front band adjuster down snug before you pull the pump out it'll hold the clutch packs in place so installation of the pump will be much easier. Just don't forget to readjust the front band after your done.