I'm with you on the plyometrics and the overhead exercises. Not necessarily because there is an age limit to them, but because I simply don't like them. And the overhead shoulder presses can indeed mess up your shoulders. Lateral raises are far more agreeable. I'm also with you on the sit-ups. It's a stupid exercise at any age, because only the first few degrees of lifting your shoulder off the ground really train the abdominals. The full range rather loads the iliopsoas muscles (psoas major and iliacus), which you can train far more safely with a hanging knee or leg raise. And it puts undue pressure on your intervertebral disks. I had two disks prolapsed and herniated in the lumbar spine. Not necessarily as a result of situps, but the latter make things only worse.

I completely disagree with avoiding HIIT. You actually should do HIIT even in your advanced age. I'm 67 and do it three times a week for 20 minutes. The evidence is overwhelmingly in favour of HIIT as THE routine to keep your endothelial function in mint condition and also your VO2max (which is one of the most reliable predictors of healthy aging). I even do supramaximal intensity intervals. It is not pleasant while you are doing HIIT, but you feel intensely well post-exercise. HIIT is also by far the best routine to get an exercise novice to experience fitness improvements in a relatively short time of, say, 3-4 weeks. And it is time-saving. My wife, who is 2 years older than I, also does HIIT at least 3 times a week. She is incredibly fit as a result. I also see this result in my clients. So, my advice is to never give up on the HIIT routine.