Extra support is obviously needed but any posts will have to be placed on piles, just placing them on the slab is probably a bad idea. The posts already in place should be on top of large piles, the same should be done for any additions.
I have no idea if it will work or not but an idea worth considering is talking to a larger hut tub company and request a quote for installing a hot tub in the proposed position of the tank. Many hot tubs are as much as 500 gallons so weight would be similar and seeing how this is probably an application most companies have dealt with before they may have some ideas on what is needed. The key is to pretend you want a hot tub there
