USBasp programmer for 28 pin DIL

That's annoying....

Doesn't look like my USBasp has the RX/TX pins wired.

Not sure I am competent enough to flash the USBasp.

Is there any way I could take the RX/TX pins of my ATMega328p and fire them through a spare UNO RX/TX and obtain the data that way?
I have an Uno set up as a programmer here.