What type of regular maintenance should I be doing on the central air conditioning unit

How did the system perform back in '96 or at least on a good charge? Ideally someone preformed all the necessary 'manuals' and it was the correct size to use. I lived in a 1700 sf apartment that was always a little hot until we switched out a 2.5 for 3. It all depends on your heat gain: windows, drafts, insulation, lighting, appliances, humans.... If you are not going to pay an arm and a leg for a professional calculation, I would charge it up one last time and see how it preforms on a nice hot day and then decide if its undersized or just neglected. Charging it back up would cost less than a full load calculation I would think. Or just go with a 3 ton. Although the problems can be just as bad with an over-sized unit, they are much less prone to present themselves then in an under-sized unit. It may cost more to operate but it will work as opposed to it almost works.

Are you 100% certain that it blows when the thermostat opens the call for cooling circuit to shut it down? Or, does it run for a good while, shut down, and then you notice that the fuse is blown? If I were you, before going down that rabbit hole I would put one more fuse in it, run it for 5 minutes or less, shut it down from the tstat yourself, and see if the fuse is blown.

If you do find that the fuse blows as soon as the tstat shuts it down, one reason it would blow after the call for cooling is gone is perhaps there is a blower keepalive timer (common in newer HVAC systems to push the last of the cold air out of the ducts) and that is somehow shorted out, causing it to blow the fuse when that circuit kicks on to run the blower after the tstat tells it to stop.