I've acquired a Miyata which appears to be from the late 70's/early 80's.

It's cream with brown lining around the lugs and has a certain period charm which I'd like to preserve.

However, it does have an amount of superficial rust, mostly running under the rear brake cable which runs along the top tube.

Is it possible to treat the rust, then, say lacquer over it to stop further problems? This would also preserve the knocks and scratches which already contribute to the bike's provenance?

Or should I just forget it and take the paint back to the metal and investigate a full respray?

Depends on how thoroughly you fight the rust spots. You have to fight them very thoroughly to be sure rust starts there again.

With repaint you're more sure for the upcoming time.

I'd say never paint over a layer of rust. Below the paint the rust will develop further.
It's more expensive, but I'd have the bike stripped, sandblasted and repainted.