According to this website, the torque capacity of the 4R70W is 700 lb-ft ... looks like Ford didn't skimp like Chevrolet did with their 4L60e, lol (about 400 lb-ft capacity). You should not have an issue with the transmission unless the transmission already has an issue.
$2000 rebuild budget is what I'd consider a budget rebuild budget. You really aren't going to get too far on that much money, especially with what you are considering to have done. While parts are going to be fairly reasonable, getting them into the engine is what's going to cost you the money ... ie: machining costs. You'll do a lot better to get your engine, tear it down, mic all of the pertinent parts (bore, bearing journals), then figure out what you are going to need. If the engine is in good shape (no ring ridge, bearing journals just need cleaned up) you may be able to get away with doing it really cheap, by just replacing the rings and bearings. With most engines which are as cheap as you are suggesting, you'll not be that lucky.
You really need to buy an engine first before you start buying parts to throw at it as well. If you can get one which you can hear/see run, you'll be in even better shape (an engine take out from a private party might do you well). Also, since you are going from a V6 to a V8, don't count on being able to use the accessories. More than likely the new engine will not accept the V6 ones. This mainly has to do with how the serpentine belt lines up with all of the pulleys. If you can get a complete pull out (engine with all accessories, manifolds, and computer) you'll be in a lot better shape.
If you do need to factor in machine costs, you'll eat about 1/4 of that budget without even thinking about it (this really depends on the area you live in, though ... machine costs can vary in price by quite a bit -- but be careful -- machinist's abilities vary greatly as well). As a minimum, you'll want to do the following to ensure you have a good base to work with:
NOTE: The following mostly pertains to a cast iron block. You cannot do most of the following to an aluminum block with your budget constraints.
- Get the block magnafluxed to ensure no cracks are present in the block
- Bore and hone the block with torque plates (you'll need the pistons first to do this correctly ... each cylinder is directly mated to a piston to ensure proper final size is achieved). Standard over bore is +0.030 on most cast iron blocks.
- Professional hot tank of the engine to get it completely clean.
- New cam bearings and freeze plugs. You can possibly do this yourself, but getting them professionally done will ensure they are installed correctly ... most shops will put them in for you anyway as part of the hot tank procedure.
- Turn crank on both the main and rod journals. If the engine has never been opened, these will be turned .010 under. A side benefit of this is with smaller journals, you can actually make more horsepower due to less frictional losses.
- To do it right, with new pistons, you'll need to get your rotating assembly balanced. You can possibly get away without getting it balanced, but it isn't worth the aggravation to have to pull it all apart again to get an imbalanced fixed.
- If you don't have a press, you'll need to have the machine shop install the new pistons on the rods, unless you buy a full floating setup.
If you plan on doing the assembly yourself, ensure you have a good torque wrench, along with all of the expendable parts you'll need prior to the start of your assembly. Things like three oil changes (plus an extra quart for miscellaneous) and filters, sealants, complete rebuild gasket set, etc.
Also, you'll need to get exhaust work done after the engine is in the car. You will find the old setup will not mate with the new. If you put headers on, there's another expense.
As you can see, the money you will be spending will not go far, even if you do most of the work yourself. I'm not saying you can't do it, just doing it right with an eye towards longevity of your build will soak up a lot of $$.
After saying all of this, I'm sure I've left a few minor things out. Just be aware as you go through your build, you'll discover things you've forgotten to purchase. It's those unexpected purchases which will nickel and dime you to death in the end.