This might be overkill, but maybe this is possible:
1) Remove the SPC700 from the SNES.
2) Designed an FPGA circuit that will sit between the SPC700 chip and SNES.
3) Rig is all up with appropriate connections.
4) Use the FPGA to spy on the activity between the SPC700 and SNES.
5) Add a function to the FPGA that can simulate the requires bus signals to drive the SPC700 directly and then trigger this using a pin on the FPGA. Use this to (temporarily?) hijack the SPC700 and do with it as you please.
6) Dump that data over some bus that the FPGA connects to.
Code:
SNES <------- FPGA -------------> SPC700
|
|
+----------> PC