Tropicals are more sensitive to temperature and depth than Hardy's?
Tropicals by nature like warmer water than hardies. Hardies usually bloom earlier than tropicals.
The warmer the water and the brighter the sun, the better your tropicals will perform.
Night Boomers... also tropicals... bloom even later usually. They usually bloom later in the season and go dormant faster than day blooming varieties.
Gradual steps in lowering the depth over the crown of tropicals?
That is the best method. If you drop a lily that was in 6" of water down to a 2' depth, it's pads will usually reach for the surface the next day. But if it is cool enough in the water, you can shock the tropical into thinking seasons have changed and it can try to go dormant or at least pout. It would be better to lower it to 10" to 12", wait a week to make sure it is doing well then lower it to 16"- 18", wait another week and if it is doing fine drop it on down to the 2' level if that is what depth you are shooting for.
The bigger the pot the bigger the plant in both tropicals and Hardy's?
Hardies spread their rhizome like a hand with fingers reaching out away from the pot. That is why you want to plant it at a side of the container growing at an angle towards the center. The bigger the pot, the better. You lessen the chance of it growing into an edge and deforming or damaging the lily rhizome with a bigger pot.
You can take a tropical and grow it in dixie cups and get a beautiful flowering specimen that might be 1' to 2' across from pad edge to pad edge. You take that very same plant, pull it out of that dixe cup, plant it in a 8 qt container and feed it well and within a month or so with good weather and warm temps and it might be 8' across with flowers that are double in size to what it was a few months earlier. Now certainly different lilies have different fully grown out sizes but the more room you give a lily to spread it's roots, the bigger it will get for you.
Tim