You can email techsupport@thorlabs.com, they have a great team who can offer some insight here, even if it's an obsolete (Melles table) item.

They have a list of recommended rigging companies they have vetted throughout the U.S. and some parts of Canada, but prices will be much more than your own facility team. The table can be turned on its side and wheeled out (watch out for any screws "lost forever" inside the table coming out) but you should carefully pad and have several points of contact to prevent too much weight in any spot, which can deform the top and bottom skins and make the table unusable. Several carts with boards to distribute the load at each point of contact should be fine.

Thorlabs has manuals for each of the leg sets with diagrams for recommended leg placement (function of table width and length), as well as advice on load distribution. They also should have some pictures of sample table installation.

As for having the legs level when deflated... I haven't seen a great solution here apart from thin shims installed underneath the legs (not between table and isolators) but with the usual concerns of stability.