Blair P. Houghton wrote:

Turns out I'd mis-measured my rear stays and they're only
124 mm. The frame is made of steel. It's reinforced by the
brake mount, so it doesn't flex much the way I need it to.
No way am I bending this frame, and I really don't want to
have anyone else do it either.

I'd reconsider if I were you. I guarantee you that whoever built your
frame bent it at least that much just to put it in its original state.

If it hasn't been deeply corroded internally, it will move again
without damage. If it has been so corroded, better to find out now
than somewhere out on the road.

I have no less than four bikes at home-- all but one of my factory-made
steel frames-- that have been bent to a wider spacing. I've had no
problems as a result of this.

Chalo Colina