Hi,
However, Port 0 still remains high for a couple of us or ms seconds

1) How do you find it?
2) How do you read port? Do you use external memory access cycle with MOVX or self-made access via extra pins for /OE, /C etc emulated with program?
3) Are both HC245 and LCD disabled correct with schematic (in case of MOVX) / program (manually manipulated bits)?
4) Are there no interrupts enabled in your program? It may be that an ISR executes after you have read port but before you disable external input and clear port.

Regards,
Oleg