Never heard of a variable converter. Got an example? Sync and re-sync really is not a factor once you get the right connectors.
Are you sure those are the only two inputs your TV supports? And there are two standards that use RCA connectors - composite and component. Composite typically has 1 yellow connector for video and stereo left and right with a red and a white connector for audio. Component is video only with red, green and blue. Audio is handled via a separate cable. You need to determine which one you have.
But also, for many, many years TVs have supported 75-ohm F-Type connectors for coaxial cable TV connections. So if your TV does not have an F-Connector, then it is time to retire that TV.
There must be something more advanced out there...w/out the cost of a new t.v. =]
"Advanced"? That's the problem, isn't it? It appears you are trying to adapt antique technology to modern. At some point, you just have to let go of the old. You can't put a modern jet engine on a Sopwith Camel
Now if your TV does have an F-Type input connector, you might look at an RF modulator adapter to go from your VGA out to your F-Type in. Another alternative may be to buy a TV Tuner card
. That said, if look for your cheapest alternative, go to a thrift shop and get an old VCR that has the inputs you need.