I'll certainly not get large AC because (a) It will make more draft. (b) It will make temperature swings, like you said. (c) Tt will be more expensive.
My two cents FWIW...
Most thermomstats are set to run +/- 2-5* swing difference. Logically...Undersize + heat wave = Your unit will have a hard time COOLING defeating why you truly have it. Oversize is the better choice all around. Yes it will kick on and off but it will not, not perform when you need it. We are also talking 2-5* degrees either way.
You can block a draft. Running consistently is not more efficient on cost.
True, and if the coils freeze over you are screwed until they thaw. Another good reason to choose the chameleons you keep based on your local temperatures. Otherwise you have to fight nature, which can get expensive and may put your animals at risk in the event of a outage or equipment breakdown. Basements come in handy for those montane chameleons in the hot summer months.
Rather than just my ill informed opinion, here's some links to help you. Lots of information on why not to oversize your AC unit. Going too far undersized is bad too because it won't keep up and can freeze the coils.
According to the second link, air conditioners operate more efficiently the longer they run continuously. Frequent cycling of an oversized unit is inefficient. Simple physics.