Okay, there are JUST OPINIONS, okay? I'm not an expert on the "weight of things" per se.
1. Don't laugh, but the original I6 setup, all things considered, could be the way to go. It's got zero electronics, nothing "extra", and an old school I6 will run and run and run. If you REALLY want to dump some weight, find an aluminum head. Granted, it's old school, it's not super powerful, and it's not going to do 30mpg, but the old I6 is a solid daily runner.
2. For a V6, eh, the old 3.8 that Ford used to put in everything is a solid powerplant, and it's got a ton of options. You can go basic plain Jane or SC for plenty of horsepower. It's just a good, solid little 6 that you can probably pick up for a kiss and a promise somewhere.
3. If you want to go light, why 6? What about a 2,3L that has a decent build? Get a little turbo setup or, if you want to go super trick, find some guy with a winning "mini-stock" dirt car, and ask him to build you a 2.3L. LOL! Tell him it doesn't have to meet spec, make vacuum, or anything else. You'll need some rearend gears, but that would be a quirky fun (light) motor. And the guy may build it for cheaps with stuff he has laying around. Who knows?
4. Find a nice "ecoboost" something or other that's been wrecked. You'll need all the copper to go with the aluminum, but if you pull it off, you'll have a SMOOTH fast car that DOES get 30mpg (or better).
I'm betting there are 100 websites with good options, probably MUCH better than mine. I was just kicking it around in my head. The good news is that, heck, let's face it, most of the V6's you can buy in a "normal" car now will run circles around a vintage V8. And if you're looking for a "wrecked" version, you have an advantage because you're not looking for a "wrecked Roush Custom Shelby enhanced IMSA banned only driven once a week to pick up his mail" car. You're looking for a Lincoln MXK with the ecoboost 6 wrecked . . . hopefully rear ended to Hades with the front just fine. The downside is that about 60% of what makes those motors so good is the electronics, and that can be a massive challenge. And, eh, in the long run, after you count the mainframe, sensor array, and cooling units needed to make a good V6 outstanding, an EFI 302 may be lighter . . . and easier.