Wow! This is exactly the kind of response I was hoping to get - clarification that that inner sleeve (I've been calling it a band) was not usually found in the Schwinn bottom brackets of that era. I figured it must be an anomaly since all the other postings about using the Truvative suggest that installing it was a fairly straightforward operation.

The guy from whom I bought the bike said it was "early eighties" but he didn't know for sure. When I got the bike three years ago I looked up the serial number and since then I've been saying it was an '82 - but the decals (long gone by now) definitely don't look like the images from the 1982 catalog. I don't have the serial number with me. I'll look again next time I get home. (I'm forced to ride my sweet unmolested early 80's Trek 500 while the Schwinn is in quaqmire status.)

I most definitely punched out the cups in case anyone is still wondering. Here they are:



So we've established that the sleeve is unusual, and that the adapter screws won't clear the sleeve.

I should clarify that the sleeve does only wraps abound about 2/3 of the inner surface. There is room in its gap for one of the screws.

As MiamiJim did here, some helpful folks on a local bike forum suggested cutting some channels in the sleeve for the screws. That was going to be my next step. But in light of Pastor Bob's theory:
It probably needed a very rigid BB shell to take the extra leverage caused by the long seat and down tubes.

I wonder if digging out a couple of paths is a good idea - stability wise?

And yes, I realize that the bike is heavy and that all this effort and expense is rather silly but I'm enjoying the process and learning a lot on the way. I commute on the thing year 'round in Chicago and it serves my purposes wonderfully without being a very attractive target for theft.

I'm super grateful for everyone's help here!