It's been a while since I played Oceania (being in the beta kinda burnt me out on it), plus going back to school at my age has rotted my brain, but I'll try to remember how I dealt with that stuff.
First, re: majors, play on bigger maps. Small maps give you oceans with too many connected landmasses and too few MTHs. But even on a bigger map, if you roll a planet where a tiny number of MTHs dominate the seas, you'll still have the problem of distant powers being able to jump down your throat constantly.
One expensive solution to this is to force an MTH split on a particular ocean zone you're trying to exclude landings in - that can sometimes stop invasions cold b/c the distant power(s) will no longer have contact with an MTH controlling your neighborhood waters. Ofc, if the MTH you're splitting is a strong naval power, it might just eat the offshoot, so that is something to consider.
Buying up all the MTH's available shipping also puts a damper on other majors' ability to invade constantly.
Re: critters, aircraft and artillery hitting them at sea helps slow them down and kill them off, but mostly you just need to keep a shore patrol. That helps for the invasion stuff too - forcing proper assaults instead of unopposed landings makes things significantly rougher on would-be invaders.
I will confess that on a few long playtests where there were particularly ugly sea critters, I may have nuked some of them. If you do it when they're far enough away from the shore, you don't have to deal with any environmental damage even if you're hitting them with ICBMs.