Speeding up your clock is one way to reduce the data loss; but it's not the only way to speed up your code. Are you seeing major flicker, or just a subtle effect?

More subtle flicker might be caused by zero crossing errors. Does your break-detect (88 microsecond) routine turn off the ZX interrupt for too long?

In any case, be sure that the receiver is never ignored for more than 44 microseconds (one byte time). The receiver interrupt must also be considerably shorter than 44 microseconds, including the interrupt and return process.

I could be wrong, but I can't see how to generate 250 mb/s from 24 MHz.