Since you have already signed the contract, your options may be somewhat limited if work has begun OR if materials have been ordered and paid for (by the contractor). That is, your options for “free changes” may be limited.
So, what you can do is… request a Change Order to “hold” the bathroom plumbing for now. You may want to amend that CO to “not install the bathtub and associated plumbing fixtures and drain” and in the meantime talk to someone like Bathfitter (or any other installer of your choosing) and request that they review your plans and make offers for what products they can install (with particular attention at this time to the plumbing requirements) so that they can spec out the water and drain fittings and locations that they would require, and work with the builder to be able to install the tub later according to a schedule that works for all of you.
When the time comes to install the tub itself you may elect to amend the CO to forego the tub install entirely (and give you money back – which will be less than you expected, you have to realize) which you can then subcontract to Bathfitter (which will cost you more than you planned – that’s the way these things go) to have them install the agreed-upon hardware.
Or when your current contractor realizes how serious you are about this, then they may be more willing to work with you. You have to approach this more coolly and calmly, though. Nobody wants to talk to someone who is frustrated and illogical (and signing when you know that you’re not ready to accept the design is illogical).
On the technical side: There’s usually room around the sides of most tubs (between the tub body itself and the decorative outer wall facing the bathroom) to run all kinds of plumbing for the water supply, so that shouldn’t be an issue. And there’s no reason that I can see why the drain can’t be at one end of the tub and the inlet at the other. (Just because that’s the default option doesn’t make it the only option.) So assuming your tub isn’t very weirdly-shaped, I really don’t see a need to do anything except tell the builder to not install the tub and fixtures themselves right now.