Naturally aspirated with a standard 3.8L Ford crank, probably around 340-370 crank hp. Using the forged Supercoupe crank and rods could be 100 more but I think you'd need to use the late model girdle on the block. Ex-NASCAR SVO block, 4.5L, then those motors ran 550+hp.
Bear in mind, the Ford 3.8L V6 and Buick 3.8L V6 are 90 degree vee designs, not 60 degree vee motors. They have quite a number of vibration issues that Ford and GM have tried to work around. In our race motors we've done a few things too to quell vibration from mounts to reciprocating balanced percentages. It's an interesting problem and one my race buddy loves to work on - he's a vibration engineer for a large equipment company so we've had some extremely expensive equipment hooked up to the Mustangs measuring various vibrational modes.
Ford's 3.8/4.2 family (and GM 3.8 too) has an iron block and ally heads. Decent motors, but not sexy and not as light as they should be were they using an ally block.
If I were considering a V6 for an SLC it'd be the Ecoboost as others have mentioned. I've got one in my F150 and feel it's a great motor. Stock the turbos are done around 5300 RPM though and that isn't a very racey engine, so you'd probably won't to change that up for something that produces some RPM. Or not - the low and midrange horsepower is great. Probably be a complicated install though unless someone has a standalone ECU to control the engine. Look at MegaSquirt and similar and see if the Ford Ecoboost has enough of a following for that to have been developed.
If not an Ecoboost then I'd look at the large V6s from Nissan. You'll need one with boost or displacement, both would be preferable.