If you go back into the old articles in this forum and the stage II forum you will see lots of info on what is a stage II, but briefly the stock 3.8 motors in the 86-87 cars used a "109" block. This can be built up to 700-1000 hp for drag racing but life at the upper end of that can be depressingly short. I don't know of anyone who has done endurance racing at hi hp with a stock block. Buick Motorsports as part of their Indy and Busch Grand National NASCAR support developed a much stronger block casting that included bosses for 6 extra head bolts per side, and were cast as either 3.8 or 4.1 L motors. One version was called the Stage I, and they were machined for two bolt cast main caps and the extra head bolt holes were not drilled and tapped so as received they only used the stock 8 bolts per side. These were off center so stock intake manifolds and accessories would line up, and used stock style wet sump oiling. Most users drilled the extra head bolt holes and used 14 bolt heads. For drag racing these might be rated at 800-1000 hp but all these numbers are just guides. The same block casting, machined for steel 4 and even 6 bolt main caps and with the extra head bolt holes drilled and tapped was called the Stage II. There were many small variations over the years involving on and off center, with or without an internal oil pickup provision, etc. Several of these have hit over 1300 hp on the dyno, maybe as much as 1500 hp. These were the blocks the NASCAR and Indy guys used, and at the 500-600 hp level would last many races and maybe even a few seasons. All of these have been out of production by Buick for several years so the supply has been steadily dwindling. There are some excellent blocks to be had, for a price, and a lot of used up junk with lots of repairs and sleeves - you definitely need some experience and good advice before buying anything. A few years ago TA Performance came out with their aluminum block, with many structural improvements over the Stage II's. No one knows what the limit is on them but I know some have been over 1000 hp already on the dyno. Apparently some of them are used in off road dune-buggy style vehicles but I don't know what the durability at full power is like. Building a very strong stock 109 block motor, buying all new parts, is going to run $10K+. There aren't many Stage I blocks left, and the Stage II is a good bit stronger for about the same price, so I wouldn't really consider one for your project. You can get a dyno tested crate motor from someone like Duttweiler for $25-35k, or you can scrounge and dig and come up with good used parts and maybe only spend $15k to get a running Stage II motor. Used Stage II motors advertised as running in good shape seem to be advertised for $8-12K and come up for sale here every few months, maybe.
The best thing you could do would be to call Kenny Duttweiler and talk with him, since he has built lots and lots of Buick V6's for lots of different applications, and can give you realistic advice on durability and hp levels. Whatever you do, please post your results as we all love to hear about Buicks in competition.