Wire wrap and breadboards severely limit what you can use of modern chips. It is a common misconception that it is the clock speed that has to be watched - WRONG, it is the risetimes and the power. I am not looking at a datasheet, so the numbers are approximate from memory:
a 74ALS raise 40mA in 2ns
a 74HC rasie 1 mA in 10ns
you figure.

Also when breadboarding/wirewrapping do not use processors with a Max clock speed above 12 MHX YES a max speed - again the clock does not matter but the max speed indicates the risetimes of the chip.

NOW here is a problem: the chips are specified as capable of a max speed of .. NOTHING forbid a mnufacturere from substituting a faster chip and label it the same (NOTE there are never any minimum rise times listed) so you may do everything right (supposedly slow uC, supposedly slow chips) and still get in trouble with your breadboard/wire wrap.

My suggestion:
Buy a 'protoboard" all will be well and you can tap the port signals off the protoboard to your breadboard (if needed round the pulses with some small RC circuits).

Erik