However during the week from Monday to Friday I have little opportunity to do much other exercise. I do a few strength style exercises like sit-ups and pull-ups in the middle of the week but as I age my body is starting to tell me that this kind of intense exercise is not ideal for my joints and that I would be better off doing some other kind of gentler mid-week exercise routine going forward. My girlfriend thinks that just going for a walk would be good and she is probably right. I was considering trying Tai Chi during the week as that is supposed to be good for the joints and general all round health and fitness.
Tricep extensions with a dumbbell in the gym using too heavy a weight and with fast, jerking movements instead of slow, smooth controlled movements.
It was many years ago and I was young and dumb.
Warm up a bit first. Start with gentle exercises like touching my elbows to my opposite knees, touching toes and doing bird dogs. Then progressing to doing some sit-ups, press-ups, and chin-ups. One set of each.
The weekend Horsey stuff sounds like ideal GPP general conditioning stuff - so really good.
With ref to the bodyweight stuff - One set maybe the actual issue.
I think its coming to the body as a bit of a midweek shock and 1 set per week is going to come out the blue as for the rest of the week you are deconditioned to it. As its only one set every 7 days.
There isn't enough volume or intensity to generate adaptation over the course of a week to be repeated with advancement the next week. ( IMO )
Leaving an exercise like bodyweight cals and doing one set isn't ideal - ( neither is blasting an exercise to the max all the time. )
As you say you are doing pullups and sit ups at home I am assuming you've a pull up bar at home.
Lets say as an example your max 1 set effort is 10 reps - all in - no extra in the tank ( with good form ) and that's an RPE of 10.
So try doing pullups Monday - Wednesday - Friday - 3 sets of 4 reps with a few minutes in between - as this becomes the norm for the next month - try adding an additional rep - so 3 sets of 5 reps.
Then 3 sets of 6 reps , etc etc
Same with sit ups - build up some sub maximal ( IE not full intensity ) efforts over multiple sets.
HTH