Some modifications are necessary in order to use a PICAXE in the Rock-Mite.
The power amplifier is keyed from pin 2, obviously, the PICAXE bootstrap uses pin 2 for serial in, as shown above. TX keying therefore need to be rerouted to another pin. Fortunately, the line for keying is easily accessible. Now, "Serial In" and "Serial Out" (paddle dot) could form a programming port for the controller (three additional resistors).
When using pin 5 for generating PWM (frequency shift), pin 3 could be used for TX keying. With Q2 removed, the gate pad of Q2 could easily be routed to the TX-line, next to the crystal Y2. Hence, the original TX-line should be cut next to the source pad of Q2.
With this mod done, the RM should be fit for a PICAXE-08(M) controller.
I will post another photograph, as soon as I did the mod.