Blair P. Houghton writes:

I got my new wheels.

The new rear hub is 130 mm wide.

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. So I'm kinda screwed at this point. I can't put
this wheel on this frame. The front fits fine.

Lay your frame without wheel flat on the ground. Put your foot on
the frame end. Lift the other one with both hands until it stays
at 130mm. Go ride. Sometime when it's convenient, have the
alignment checked.

Let me add to that to place your foot at the brake bridge of the
side on the floor and pull up on the dropout that is upward with
care, noting when spacing has increased by about half the distance.
Then repeat on the other side. Overshoot isn't good.

At this point the dropouts are no longer parallel (if they ever
were) but the angle is smaller than you want to know about.

The mechanical theory is sound.

But I've got enough practice with mechanicals to know that theory
don't mean **** when you're standing there with a broken widget in
your hand.

Huh? What is it that you think will not work?

I'd rather find the right axle or find out it's not possible to find
one, first.

It's not the axle but the width of hub and freewheel that defines
frame spacing.

In this case, repacking the bearings is much the less-stressful
solution.

Or, rearrange the deck chairs as the ship sinks. What does this have
to do with the OP's frame width adjustment?

Jobst Brandt