I am the first to admit that my google fu is atrocious. I have lost my ability to properly(or improperly for that matter) adjust centerpull brakes. I went to Sheldon Brown's website and found them to not even to be listed as an option. I also found out, to my horror, that Harris Cyclery has closed. I always enjoyed doing business with them. And as I type this I have realized my problem. I need one of those hangers that slide over the steerer. I'll see if I can scare one up. Or I'll look at other options for caliper brakes. The issue being finding calipers to reach a 700C rim on a bike built for 27". I have a set of Tektro long reach, but they are of the non-nutted variety. I can't remember the proper term, but you know what I'm talking about.
And this all comes down to the recent decision to move forward with just two road bikes. They both have to be in top condition, because there is no more "oh I'll just grab another one today".
Thanks for hearing me out. I might not have figured it out without writing it down. Have a wonderful week.

https://www.benscycle.com/dia-compe-...hoCYboQAvD_BwE

Porkchop BMX may have that.

Thanks for the suggestions. All I needed was to get my mind opened up a little bit. And writing did that. I noticed a shallow groove on the inside of the Dia Compe calipers, that wouldn't allow the pads to slide all the way down in the slots. So I changed out the pads, and for good measure filed the slots a mm or so too. That gizmo from Ben's Cycle looks the schizz. I might just get one just to have around. In this ongoing saga--Sunday afternoons--I put down my 8mm wrench a couple weeks ago and never saw it again. This same occurrence befell my Park Tool needle nose pliers over a year ago. I recently bit the bullet and bought my third pair. The first grew legs and walked away. I was able to make use of the dumbbell wrench I inherited from my dad, for those 8mm nuts on the brake pads.
If you all are lucky you will live to be old and forgetful like I am. It's no fun to be constantly losing things. All of today's tools are accounted for. Barely. There was a moment of angst when the 10mm couldn't be found, briefly.

ParkTool has a pretty good video for refreshing your memory.

I got this gizmo in a lot of old bike tools a few years ago, it makes setting the brakes up easy. I will keep running 27" tires as long as they make them.

Disconnect the springs while adjusting. Makes life simpler.

My third hand is a C-clamp that puts the pads against the rim while I take the slack out of the cable at the yolk and cinch it down. Rarely do I need to repeat. One of these days, I’ll get a trigger clamp.

My third hand is a toe strap! Also comes in handy as a parking brake ( either on the brake lever or strapping the front wheel to the down tube).
As for the missing tools, we usually attribute that to those evil Bench Gremlins…..

This is what I use, too. Easy peasy.

I hope someone told you to make sure the brake shoes are toed in so when the friction tries rotating them they end up being more parallel to the rim under braking force. On my old junky ten-speeds I ride I carefully bend the brake arms so the trailing edge of the pad is about one-eighth of an inch off the rim when the front of the pad is just touching, but depending on the material your brakes arms are made of and their quality the amount of toe will vary.

What brand and model of centerpull?
there are a few basic commonalities
the third hand or substitute helps much but that is not all depending on the brand.

one note - Do Not attempt to toe in Universal brakes of any type. Fractured aluminum will result.

Why not set toe with brake pads that can set toe? Are new brake pads really that offensive