"could I just cut the main cable and let the enrichment valve's springs do their job of closing the valves, and leave it alone until I can repair/replace the frozen cable?"
that is what I have done, is working good so far, I put some silicone where the cables used to go in, it was sucking vacuum in, and I didn't want dirt in there. I do worry about being able to start when the weather gets colder, but for now is starting fine, no throttle till id putts to live, then just enough to keep 'er going till warmed up, not as hands free as I would like, am thinking of machining choke knobs for myself, might end up selling them, this seems to be a common problem on the VT700, and possibly others of this vintage.
1972 Honda CB350 -gone
1967 Honda CB160 -gone
1982 Honda CB900 Custom -gone (sniff)
1972 Honda 550 four -gone
1982 Kawasaki 440 ltd -gone
1983 Yamaha Maxim 750 -gone
1973 Suzuki GT750 -dead
1984 Kawasaki 440 ltd -dead
1986 Honda VT700c -resurrecting