Welcome to the PICAXE forum.
You could generate your own 'servo frame'; send a pulse of desired width then pause for the rest of the frame time. Your timebase is a little out, the SERVO value is in 100th's of a millisecond so for "SERVO pin,100" that would be a 1.00ms pulse in a frame of 20ms so on a 4MHz PICAXE that's roughly equivalent to ...
Do
PulsOut pin, 100
Pause 1900
Loop
Adjust the PULSOUT time and you've still only got integer steps, but increase the PICAXE speed, double the values to keep the same timing, and each step becomes half what it was.
at 4MHz
PulsOut pin, 100 ' 1.00 ms
PulsOut pin, 101 ' 1.01 ms
at 8MHz
PulsOut pin, 200 ' 1.000 ms
PulsOut pin, 201 ' 1.005 ms
PulsOut pin, 202 ' 1.010 ms
at 16MHz
PulsOut pin, 400 ' 1.0000 ms
PulsOut pin, 401 ' 1.0025 ms
PulsOut pin, 402 ' 1.0050 ms
PulsOut pin, 403 ' 1.0075 ms
PulsOut pin, 404 ' 1.0100 ms
And upwards as you increase speed.