FWIW, I don't bother taking my mower off to use the loader. If I'm lifting things with forks, cleaning out the barn, or dumping compost on the garden I don't leave the lawn or driveway so clearance is not an issue. What IS an issue is weight with a full loader so I will routinely hook up the ballast box or my tiller for counterweight. Depending on the weight of the 3pt mower that might do the trick, but a box is shorter so watching the loader swing around can take focus. (I know I'm constantly looking around with my rear blade, and I assume a mower sticks out about the same.)
As for the deck, the Massey's have a height adjustment for the deck. Spin the knob all the way up and it locks the deck from dropping with the 3PT. The deck also drops further than the 3PT, so you can lower the deck and still have the 3PT implement off the ground (and lift it a few inches before the deck lifts with it).
Edit: There's also a 3pt lowering speed adjustment knob. Tightened all the way prevents the 3pt from dropping. So it can be raised part way or all the way and "locked" in place while the mower is dropped.