I agree that 6 weeks is probably too long. I would (and do) take about three weeks off and then return to the bike, doing mostly long steady rides during the winter. I do feel the benefit of taking a complete rest - about a week into it I realise how tired I was without knowing it - but that may have something to do with the fact that I am getting old! And I'm a fan of cross training. Running doesn't do much for your cycling-specific muscles, but it makes it easy to get a solid workout in less than an hour and I have a theory that providing the core muscles in your legs with the different sort of workout that running provides helps prevent muscle imbalance and may protect against niggling injuries. I can't prove this, of course, and it may be totally unscientific. But since I stated running once or twice a week as well as cycling I feel stronger.
Winter is also a good time to work on core muscles. Never a bad idea and adds variety. Interestingly for us cyclists, the
bicycle crunch is said to be the most efficient.