Is a "self-bootstrapping" zero-crossing AC power switch possible?
You can design (or buy) an SSR with a 120VAC control input and zero-voltage switching output. Anything more than a few amperes will need consideration as to how to get the heat out. Probably run you $20-$30 for a safety-agency approved unit from a good maker capable of a few amperes (like the dimmer you mention). 

Designing it could be accomplished with a zero-voltage switching triac output optocoupler with a mostly capacitive dropper and bridge rectifier at the input. The optocoupler would drive the main triac. Nothing would be isolated from the line in such a design, so proper care would have to be taken or it could easily be unsafe. 

Such an installation (including the use of a UL/CSA approved SSR) may well not conform to code requirements and you'd be well advised to find out what your local regulations are- both for safety and to ensure your insurance coverage is not compromised.