It sounds like you’re not warming the head joint up enough. I stick the recorder down the front of my shirt, upside down with the top surface of the beak resting against my chest, for at least 10 minutes before I begin to play. That warms it up much better than my hands can do. I might get some condensation in the windway after a while anyway, but definitely not once every minute, and certainly not very much.
This was something that really caught me by surprise when I started playing very recently. I’ve struggled with the same thing with my Yamaha Ecodear, which leads me to having to practice clearing it. So far my favorite method of clearing it is to put a finger over the top of the fipple, but still leaving the bottom open, which prevents it from making any noise, but lets me blow really hard. I don’t know how the more experienced players here feel about that, but it seems to work, and I prefer it over sucking the spit back in. 🙂
I’ve been considering putting my recorder under an electric heating pad for a bit before playing it, though I’d want some kind of temp control so that I don’t over-heat it.
If it’s a plastic recorder, you can also either rinse through the head some water with a bit of dish soap, or take a piece of waxed dental floss and see-saw it through the windway to get some wax in there. (Tricks that come from the pennywhistle world, but it works for my recorder, too.)
You could take a look at Sarah Jeffery’s video on this subject:
The only thing about it I don’t like is that she doesn’t point out that the only way to temporarily get rid of the clogging WHILE PLAYING is by sucking. She makes it sound as though they are equivalent methods and use the one you like best. I find that blowing is more effective when it gets very clogged, but, as I said, sucking is the only practical way to do it while playing. You can see players doing it when there’s a moment where they aren’t playing.