I'm not sure what orientation you're printing it at but you could try organic supports, those usually take up less surface area. Unfortunately with supports you're always going to have a rougher surface than printing without them
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Also in this case it might make sense to split the model, then glue it together.
Here’s the top side for comparison
There might not be a good way to escape support artifacts on the print surface for large, irregularly shaped prints. You can certainly try organic supports, but you might want to look into post-printing processes to improve the look and texture. It's more work, but it might get the result you want.
I know its late, but in the future try using the support interface feature, its like a raft that replaces the final layers of the support beneath the actual print, it won't look as good as the top side, but you'd be surprised how much it can mitigate.