So what do I have going on here?

[Spanky]

OK, so now the question is, can these be adjusted in any way?

It looks like the adjustment is by tightening the center nut on the shock body, increasing pressure on the star spring, which increases the internal friction and thus the effort to move the shock arm. It's kind of a trial and error process to get it to the point where the damping effect on the suspension feels right, something you can look forward to when it's all back together!

 

[HenrysT]

You might need new friction material ... something like this > Garage Sale - Replacement Friction Material for Speedway Friction Shocks

 

[Hackerbilt]

I had poorly positioned friction shocks with a single friction pad on each shock. Didn't work so well.

Made shorter arms and moved them out closer to the wheel (mine were side to side not front to back like yours).
I also redesigned the outer plate to mount to the chassis so I could run two friction pads on each shock...and used a pair of Blazer door hinge springs to preload my shocks so as not to have to continually adjust them.
They worked great and after installation I never had to readjust them in 3 years of summer driving.
BTW...for friction material I used some rubber discs I cut from a piece of rad hose.
Just cut it lengthwise and flattened it out to cut some discs.

 

[timothale]

The Hartford shocks have a pointer and a dial on the front plate so you can set the tension. Hartfords use wood for the friction material. about 15 years ago when I was putting my hartfords on the speedster replacemane parts were available in the UK