mold under the tub

We have been very happy with our tub, but we have one problem we are trying to solve. 
Our tub is not direct plumbed to the drain and is in a room with our main shower.  
Because of the configuration, water builds up behind the tub and drains very slowly.  The water build-up causes mold on the tub and on the floor around the tub. 
To stop the water build-up we wanted to raise the tub by putting blocks at the four corners and let the water flow through.  
 We are concerned that this is not enough support for the tub. So how much support do we need?
Thanks

It is nice to hear from you!

if your floor drain cannot keep up with the water being discharged from the ofuro, one solution is to reduce the flow from the ofuro by partially closing the drain.

1) You can just leave the plug partially inserted,

2) or you can close from the back with silicone caulk half of the opening. Of course in this case it would take more time for the ofuro to drain, I do not know if it is a problem for you.

3) Another option is to attach a plastic hose to the drain and insert it into the floor drain. This should already reduce the flow amount, also it should avoid water build-up.

4) about raising the ofuro on blocks; there is no problem with blocks under the 4 corners. Be sure to place the blocks so they support the sleepers under the long sides and not support directly the bottom of the ofuro.

5) lastly, an idea to reduce the residual humidity in the bathroom is to place a fan or a circulator on the floor and let it on for an hour or so after taking a bath.

Natural ventilation is the best solution to prevent mold but just making the air move is definitely a very good surrogate to improve the performance of mechanical ventilation.

Please let me know if these tips improve the situation!

All the Best//

iacopo