IMHO - at this point - doesn't matter what oil you use, you need to make sure the crankcase is full as often as possible.
Oil changes - still need to change the filter at your original interval, no matter what is happening with the oil and frequency of makeup oil. If you want to change the oil and filter at your current interval (5000 miles) - that is perfectly fine. I understand that you might feel the oil life is OK, since you are refreshing it so often with makeup oil - but the bottom line is that you still have the change the oil and oil filter at some point.
Probably more convenient to just do a regular oil and filter change every 5K miles. Trying to change just the filter with a full crankcase is tricky for even seasoned DIYers - would save time and effort in the end to just change it out like normal.
"Why does the car burn oil the more you drive it and burn less the less you drive it" - you're kidding me about this question right? This is just operational common sense. Oil consumption is directly tied to engine usage - the longer the engine is running, the greater the likelihood that it will consume more oil during operation. If oil loss is happening only when the car is not driven as much, then this will indicate a physical leak - at this rate of loss, should make for a considerable leak spot on the floor.
Piston soak - sounds like a typical procedure for piston soak. Still, that doesn't tell me what solvent / product they used. Draining the product out is unusual - usually the solvent will seep past the rings and be in the crankcase oil, or if it didn't - they usually run the car to burn it off. Possible that they added more solvent than usual, and needed to siphon it off to prevent hydro-locking the engine.
If they used something like (MMO) Marvel Mystery Oil - that won't do much to dissolve carbon around the piston rings (can't get too it, too viscous), but will help with carbon on the piston crown (does not influence oil consumption). If they used something considerably less viscous, like Berryman, Kroil, petroleum based light solvent - those "could" get at the rings and oil drainage holes. Drawback is they have to keep track of how long it was soaking, as those solvents can be quite corrosion to internal engine parts. Berryman, for example, will eat aluminum after a length soak.
To me, piston soak = 5 weeks no consumption could be just coincidental. Sounds like the car is intermittently consuming oil depending on engine load. People who have experienced excessive oil consumption have reported that the engines seemed to be running perfectly, oil levels in check - then almost overnight, oil levels dropped a quart or two.