You should be able to take the serial straight into the B.2 connector pin between PICAXE and Darlington Driver. I would predict the Darlington won't affect the signal. If it does you can take the Darlington out of its socket completely, cut the particular leg off or gently bend it up so it doesn't make contact with the socket.
Another alternatively is to stack DIL sockets with the appropriate pin/contact pulled out of one so there's no circuit through the sockets for B.2 to the Darlington.