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Your heater core is clogging up, and only flowing in the upper section of the core. You can disconnect the hoses in the engine bay, and try flushing it out with alternating blasts of shop air and then water (cover it with a rag when you blast with air, water and gunk will fly out all over)
If you can't get it clear this way, then you need to pull the dash and replace the heater core.
Correct, you have flow through it but there is a portion of the core that has sediment or something sitting in it. Take a look in your coolant reservoir and see if there is any sign of anything sitting in the bottom of it- that would give you an idea of what may be in there. On different vehicles, I have seen sand (from the initial engine casting) or rusty sediment, or just the coolant "gelling" up, which can be a problem if you mix coolant types. There are some coolant system cleaners, you could add that to your system for a while and let it work to break down any residues, then do a full coolant system flush and refill. I have found that Mercedes makes the best factory coolant, but VW coolant is pretty good as well. American car makers have coolant that gels up.
But it did make a difference to the driver side? I know what you are saying about not being dual zone, so there is no issue with a flap being stuck on one side but not the other- it's more a matter of where the ducting splits to go to each direction, and how the heater core "straddles" that split. I think if flushing had an effect on the driver side, that you are on the right track, it just may take some more flushing. Were you able to visually see what kind of residue was coming out of the core?
Yes, as it clogs up the fluid just goes "less deep" into the matrix, until eventually it is just passing across the top of the matrix to exit right back out! Like you, I think it would be better if it HAD to take a long convoluted route through, and maybe incorporate a bypass ONLY if it clogged up, to avoid blowing it out due to pressure. But this is what we're stuck with. I hate pulling the dash to replace a heater core unless it is physically leaking, so I try to flush them as much as possible.