I would not travel in high winds if:
I had a long way to go
or
I knew there was a risk of grounding in that particular part of the canal
or
people were fishing!
Dealing with the wind by itself is ok but the combination with shallow sides would put me off.
Otherwise I would do it. If you were cruising in an area where stopping was not recommended then you would press on and this is no different.
Don't try to cruise slowly in the wind, just go for it. Only slow down if you reach a point where you are going to hit something that you ought not. Taking off may be difficult as you have indicated. It may be necessary to walk the boat past neighbours to start.
Bizz, can you devise some sort of strap on keel for us?