dc42:
- In your circuit, what are the MOSI, MISO and SCLK pins connected to, apart from the ICSP header?
They go to another similar header that is connected to a nRF24L01+ 2.4 GHz radio. Although I often disconnect that when programming, because if I start programming right when a packet is on the wire, the radio confuses the programmer.
- Do you disconnect power to the H-bridge when you have the ICSP programming cable connected?
Nope. Hence, why this is my prime suspect 
I'd love for a programmer to be robust enough to not need that, though. TVS-es and current limiting resistors on all wires, buffering, etc. Maybe some parallel caps, too, for filtering. The USBtinyISP actually has buffers, but not TVS-es -- if you blow something, it's more likely the buffer than the 2313.
I just want to make sure I'm not overlooking something else.
FWIW: I hadn't noticed how extremely current hungry that pair of motors is (it's two motors on one H-bridge) -- my bench power supply drops from 8.2V to less than 6V when they start, even though I'm using PWM, and the current limit is set to 5A. On battery, I don't have that problem -- yay for high-C LiPo packs And also, yay for MOSFETs that can take > 20 A