In re the kicking at the safety stop -- having to kick to avoid sinking does not necessarily mean you are overweighted. It means you are negative, just as having to kick at any depth in order to avoid sinking means that you are negative.
Most people try to weight themselves so they are neutral at 15 fsw with 500 psi in the tank. I don't, because I want to be able to control the subsequent 15 feet of ascent, so I add a couple of pounds. Therefore, if I had no gas in my BC or drysuit at 15 feet, I'd sink. So I add a little gas, and voila! I'm neutral, and not finning. This is the skill you need to master.
If you have access to somewhere where you can do some simple, shallow diving, burn up a couple of tanks playing with this. Get yourself into maybe fifteen feet of water. Try to hover five feet off the bottom. See how quiet in the water you can be. Try exhaling, and see if you sink. Try inhaling and breathing with your lungs full, and notice that you rise. Go up five feet and stop, and hover there (you'll have to adjust your BC!) Just play with various spots in the water column, with being neutral and then deliberately going positive or negative, and then reestablishing neutral at a different depth. It may not go smoothly at first, and you may have some splats into the bottom, or some corking (which is why you do this shallow!) but time spent playing with this will pay off handsomely in more relaxed, more enjoyable dives.
A good, formal weight check at the beginning of this session will help a lot, too.