That slow flexion/extension full range technique is what I've been trying for a few years. Works pretty well.

I used to do full pushups, including feet up/head down pushups during my usual 5-7 mile runs, stopping about once a mile to do 20 or so pushups. But a year or so ago both of my thumbs popped out of joint at the base near the wrist. Unfortunately I've developed the same type of arthritis and joint weakness my granddad had. So I had to switch to easier inclined push-offs -- leaning against a guardrail or other elevated surface, or countertops at home -- to avoid further strain on my thumbs and wrists. Much less effective.

And I've used rubber bands in various strengths. They're okay but the inconsistent resistance is annoying, and it's difficult to get much range of motion without needing to farm-rig a support for one end of the bands -- a doorknob, chair, whatever.

I thought about trying a door mounted pullup bar, then remembered the last time I tried one it nearly ripped out the door frame in my old apartment. My current apartment has much stronger steel frames and jambs which would probably hold up, but those makeshift chin-up bars are a PITA.

My insurance includes free membership to Planet Fitness so a few weeks ago I started working out there. I can use most of the machines without straining my thumbs and wrists, and use the same slow technique, flexion and extension. I've made pretty good progress but I'm taking it slow while my muscles adapt to unfamiliar exercises. I haven't used any weight machines or lifted weights in more than 40 years when I was an amateur boxer and in the military. Back then I could crank out 20 or more pullups, easy. Now I'm lucky to finish three before needing a rest.