There is no “one-size-fits-all” solution, so it’s hard to give a definite answer, but I have 500 mOhm on my board and I’ve used it with a design that had about 65% LUT utilization without problems.
BUT, keep in mind that utilization is far from the only thing which determines power consumption. Other variables include the clock speed and how often all those LUTs are toggling. And some Xilinx primitives can use a surprising amount of power (MMCMs in particular come to mind; for example I have a design with ~20% LUT usage, but I’m using 5 MMCMs and the MMCMs are estimated to account for almost half of the total power consumption).
If this is the design that you’re having trouble with in this thread, then keep in mind that the utilization numbers that you’re seeing are not accurate if Vivado is optimizing logic away; they could go up a lot once that issue is resolved.
Finally, just to make sure, what is making you conclude that the 35T is not suitable for your design? Are you getting an error message of “not enough resources available” when you try to generate a bitfile?