When resetting the inner limit isn't enough
 

I'm reviving a friend's beloved 1980s-vintage Trek 420 (she rode it across Europe in her 20s) on a tight budget. I replaced her worn out 126mm Helicomatic hub/freewheel with a cheap 130mm threaded Dimension replacement wheel and installed a Shimano Tourney (MF TZ20) freewheel. It's a snug fit in the dropouts, but I didn't have to bend anything.

Here's the problem: When I went to adjust the shifting on her Simplex derailleur, I could get the out limit to line up, but the inner limit stops just shy of allowing the chain to shift onto the lowest gear. Close, but no cigar.

So I'm wondering if I could fix this by playing around with spacers on the axle, just to move the cluster a couple millimeters toward the drive side. The option is I just eat the cost of this wheel and spend more to replace it with a 126mm 630 ISO wheel.

Thoughts?

I'd be trying a different derailleur before going the wheel route again. Cheaper anyway.

That's what I would do.
And then dish the wheel a few mm to get it centered.
Hopefully you won't have issues with the chain & drop out interfering.

Ah, you can envision the fix, excellent, you can also shim the "cog" out further on the axle without moving the wheel out of the centered position it was hopefully laced for, just be sure the rear whell can't move after it's secure, but I'd replace the rear simplex and cable...

Remove spacers from the right side of the axle until the 1st cog is 3.5-4mm away from the inner dropout face. Put these spacers on the left side of the axle. The rear-derailleur won't have to move inwards as much to reach the largest cog. Another benefit is your wheel will have less dish for closer left/right spoke-tension (once you've re-dished the wheel).

Why add the spacers to the NDS?
He's already sticking a 130MM hub into 126MM drop outs.

I don't think that RD was original to a Trek 420. An inexpensive Deore or Alivio RD should have plenty of travel

Reduce dish for a stronger wheel. I make all my wheels 130mm regardless of which bike it goes into. In this case with a freewheel hub, removing as much space from the right side as possible will reduce the length of the lever that's outside of the right-side bearing.