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In order to ATTEMPT to keep time, I try to establish an "inner click track" of smaller note values.
For example, on the frequently recurring "dotted quarter - eighth - quarter - quarter rest - repeat"-vamp, I might think in eighths or even sixteenths.
The slower the vamp goes, the more important that inner click track becomes and the smaller my inner subdivision will be.

It seems harder to mess up time if space between adjacent notes is small...

That’s a good technique (more subdivision)
For those who haven’t developed what you have developed, a strong/clear memory of a rhythmic song – as suggested in the original post – can serve as a way to develop this, as deviation from a strict tempo will clash with the memory of the song.

When I’m subdividing - as you suggest - during a very rhythmic piece playing in an ensemble, it feels a lot like “floating“.