Okay, so I'm unable to submit a .3ct TAS file to TASVideos (which really shouldn't be a surprise.) Instead, I'm uploading the .3ct TAS file as a .txt file in my userfiles.
How to run this is the TriCNES emulator:
Step 1, download it and rename it to "SMB3_IntercycleCartSwap.3ct"
Step 2, inside the TriCNES emulator, click the TAS dropdown, "Run .3ct TAS".
Make sure you don't select "From RESET".
Step 3, click the Load Cartridges button. If you are missing any ROMs needed to run the TAS, put them in the roms folder.
Step 4, click the Run TAS button, and it should all work out.
What is this? See the following: