OK so here's an update with some stupid fabrication that no one is likely to see except for here.
I got my wife to help bleed the brakes like Danny said—hard pumps and such—and while she kicked those pedals I noticed just the slightest bit of movement on the front firewall/pedal bulkhead.
As many of you know, that item on a Beck or TR car is an eighth-inch (3/16 maybe?) steel angle plate welded between the frame rails, whose top rises several inches above the tops of the tubes. It's plenty strong enough, I guess, but then to make my clutch pedal more "realer" I sectioned mine and welded those big chunks of it back in with the 220 AC stick machine which, although a good job for me, probably did it no favors, strength-wise.
I could see it flexing, boys. I did not like that.
So I decided to make a brace tying the top of that plate, right where the clutch and brake pedals attach to it, to the lower tube of the beam, seven inches forward. Seems a good spot because it's also where the beam tubes attach to each other with that big channel piece that you'd ordinarily use to fix the beam to the frame head on a VW pan. Strongest spot on the front axle, I'd guess.
I designed a triangle brace V-ing from inside that channel (thinking I'd bolt it to my swaybar bushing mount) out to a bit of angle bracket I'd affix to the back of the bulkhead.
Then I started rummaging through my bucket-o-scrap metal hunks, CADing things out and shining a light up under there while trying to make more junk fit.
It's really tight up there in the space above the master cylinders and below the tank and steering stuff. Especially when you're trying to fit your hands in there with whatever you're trying to improve matters with.
So after simplifying and adding simplicity, I ended up with this.
The curved part rests on the lower beam just behind the channel; the tube is centered on the beam. The bottom nut is fixed and welded so the bolt turns to adjust the tension. The middle nut is there to give your wrench something to turn, since the bolt head's gonna be shrouded.
It fits parallel to the ground. I have a bit of heavy C-channel that bolts to the bulkhead with a couple 1/4-20s.
Then I welded this sway bar bushing washer to the bolt head, to tighten up the fit in the channel.
I'll test fit it again tomorrow and, if it's good, drill small holes through the bolt head and the edge of the channel so I can wire it tight once it's adjusted. Not as good as a turnbuckle with a lock nut, I know, but I'm hoping this will be a one and done.