Any gamers care to weigh in on whether the latency added by digitising, optionally encoding and decoding, and then playing back the signal is likely to be a problem?
TBH, emulation seems like a better approach for old games. Unless authenticity is important, in which case you'll be wanting authentic display hardware, surely?
But yeah, I'd go for the composite output mod. An alternative approach would be to see if you can dredge up one of those tuner boxes used for turning a composite-capable monitor into a TV, like the now legendary Philips AV7300.