If you don't want to spend the money, say so. Most would buy an inverter w/ a remote switch on it. Otherwise switch the DC input to where ever you want it..
To install a 30 amp ATS, chop the shore power cord, and bring both ends to their place on the ATS, Then bring the inv AC output to the 3rd spot on the ATS. You're done w/ that.
Now disconnect the 120v converter circuit from its existing source, and connect it to the shore power terminal on the ATS, so its powered in the shore power position only. I installed a 15 amp inline fuse in the hot wire to the converter.