There shouldn't be a limit on naval range, the need to maintain naval superiority should be the limit. If you can keep a large task force constantly patroling the waters for weeks before the invasion, you should be able to invade all the way from San Francisco to Tokyo if you want. If you can't maintain a large task force in the waters before the invasion, you shouldn't be able to invade Calais from Dover.
I think that there should be a rather severe limit on the range of amphibious invasions.
Like, starting at about 50m for infantry & 3m for an AFV.
BUT
If you’ve got the requisite technology levels & ocean-going invasion ships, crossing an ocean to put troops, or even tanks, on a beach (like Kota Baru in Dec 41) is not at all impossible. In fact, as has been proven, it’s not really that difficult at all.
On the other hand, if you
don’t have the tech’s & kit, then you end up looking stupid like Sealion.
Casualties, attrition,
supply* are all dependent upon the level of resistance & the level of training & experience of the invading troops. Heavier troop types getting really heavy penalties until, again, the appropriate research & construction has been completed.
** apparently, once you’ve built a tank, it will run for ever. So the few hundred miles worth of fuel a… let’s say a Sherman during D-Day, landed with becomes largely irrelevant as long as you land it somewhere that has nice roads/infrastructure.