Front brake isn't bad, but the rear is quite mushy.
Straddle cables are brand new, and a bit loosey-goosey...is this the problem?
Or, the levers are vintage 105's...are they a bad match for these brakes?

PS...I'll be switching those nuts to acorn nuts, in case anybody was about to say something.

Levers should be okay for this. Have you made sure the rear cable is moving freely?

The solution is too simple.

Cut the straddle as short as possible. The problem is that the rear brake has low profile arms to ensure heel clearance.

If you look at the photo, you'll see that the cable is pulling the arm upward, while it's direction of movement is inward. Shortening the yoke cable will have it meet the arms at right angles, at the critical point where the shoe is engaging.

BRW - the front yoke cable is also too long, but since you're happy with it, you can leave it alone.

What do you mean by mushy? Too much friction? Feels spongy to your hand? Doesn't (or does) brake well?

I was excited about this solution but, alas, it did not help.

The front yoke is up higher to clear an Origin 8 Classic front rack, with custom rails.

Spongy.
The pads engage early, but then the lever depresses further...all the way to the bars if I squeeze hard enough.
The brake cable is a stainless Aztec, the straddle cable is generic.

Too much slack in the straddle cable as evidenced by the gentle bend at the yoke. Shorten them up so the caliper pads are almost touch the rim.

Agreed, oddjob.
I've now got the rear yoke quite short, and still have the issue.

I keep riding it up and down my street, braking, to try and stretch things taut.
Unless a brilliant solution arises, I'll keep trying that.

That means something is deforming or compressing as you squeeze harder.

If you really just want the lever not to hit the handlebar, take out as much free cable and reduce the tire clearance as your wheels can stand. It won't make the lever less spongy but it will give you more lever movement capacity.

Sponginess can come from several sources. Long cable runs always feel worse than short front ones. Housing ends that don't fit well into whatever stops you have can be a source. Make sure the pads hit the rim square on so that they don't deform after they first contact the rim. Make sure the cantilever pivots are solid. Anything that gives the lever higher mechanical advantage at the caliper also produces more stress in the components and more tension in the cables, which could mean more deformation or stretching. For that reason, shorter straddle cable could actually make it feel worse if you don't need that much mechanical advantage to get sufficient braking.

https://www.sheldonbrown.com/cantilever-geometry.html

I added the reference to the front brake as an aside. Your problem is in the rear, so that's the one on which to try my solution.

Normally you'd have nothing to lose, but it seems that you cut the main cable too short, so you have to gamble the price of a new cable.

I don't think you'll get those levers to be as responsive as they would be with caliper brakes.

Nature of the beast.

I'd always read that 'aero levers are always better.'

I put some Aero Gran Compe levers on my Trek 720 with Shimano MC-70 brakes- and the braking was not as nice as it was with the old non-aero 6200 levers. Go figure. So I guess that's more like 'aero levers are sometimes always better for some bikes with some brakes.'

I'm making some progress.
Took out almost all toe-in, and have been working the the levers/cables every time I walk by.
Still mushier than I like, but probably the nature of the cantilever beast...as some have mentioned.

How old are those pads? I never liked those Shimano pads when those were brand new. If they are old, they may be part of the problem. I use Kool Stop salmon as the replacement on all my brakes these days.

Pads were possibly original, although not that worn.

I had some brand new Tektros, so I put those on, and they are much better.
The front grabs really quick, as usual, and the rear is coming along.
I think after some use the straddle will straighten out, and be fine.