I finally installed my new rear tire after 2,000 km (estimated) life time of the previous one. the front tire is still in good shape. maybe the rear one wore done faster because I always rode with little air pressure? (also of course the rear tire has to bear 70% of my weight plus 100% of any luggage)
I also cleaned and regreased the chain - has been 18 months and one Torontonian winter since the last time.
pulling out the rear wheel is fast now, since I tuned the brake just right for this when I changed the patch last time.
Now let's hope that no further repair is needed this summer!
Update: cleaning the chain and rear cogwheel apparently got some dirt into the gear trigger, so that the gear hub worked really badly. I had to take it out and clean it, too. On that occasion, I also readjusted the headset and the rear axle (including regreasing of the bearing). Now the steering works noticeably better and the gears also work better than since before I started my spring repairs. Now Speedy and me are truly ready for summer!