Global/Regional Clock Assignment

Now that you've described it, I stand corrected. Putting it on a regional just might help. It sounds like you've already done it, but go to the assignment editor, put the input pin name in the To column, Global as the Assignment, and Regional(or dual-regional) as the Value. That should work.

Putting a PLL on the clock should work too, if it's available.

(Are you coming in on a dedicated clock pin? That could be a problem too, since it if's a regular I/O it would have to route over to the global drivers. If the board's laid out there's not much you can do about that, but something to be aware of.)

Finally, where do the "other clocks" originate from? Are you sure they're synchronous to this clock? If a clock comes in a pin, doesn't feed a PLL(which can generate multiple clocks), then usually that domain is asynchronous to other domains in the device. Just something to be careful of.