Slime tubes basically work, but you need to be cognizant of their limitations:
- If you expect to "run flat" through a lumberyard you will be seriously disappointed. If you expect to be able to pump up a flat a limp a mile or so home or to a better spot to fix the flat you will likely be pleased.
- The sealant degrades over time. If you have a flat early in the life of the tube you will likely be very impressed. You will not be so impressed if the tube has been on the bike for two years. I'd recommend replacing slime tubes at least once a year.
- The tubes are thicker, which is good because that makes them more puncture-resistant, and bad because it makes them heavier.
- Over time the sealant inevitably clogs up the valve. This can make it difficult to impossible to add or remove air from the tube.
- Patching a slime tube is a little more complicated. You need to bring some alcohol cleaning wipes to clean up the latex to get the patch to stick. While I've patched Slime tubes, I've never felt very confident in the patches and I didn't use the tubes any longer than I had to.
So it is kind of up to you and you ought to try them and see what you think. From my standpoint, there are lots of dials on the tire/tube machine and you ought to consider the whole problem holistically. As you have pointed out, we are all different and will come to different solutions.
For myself, I purchase spendy high-end e-mtb rated tires with puncture protection built in. I purchase decent inner tubes. I fussily check tire pressure before every ride and often multiple times during the day. I aggressively replace my tires about every 1500 miles. That has worked well for me, and I seem to get about 2000 miles of riding between flats on average.
As for flipping the bike over, if you carry a windbreaker or a rain jacket that will be plenty to pad the handlebars and display when you flip the bike over. The trick is to wrap the handlebars with the windbreaker before you flip.