This mechanism you describe does not makes sense.
Most PCV is filtered inlet port air, ring bypassed upper volatiles and fogged oil vapour.
Also the PCV is just a metering port, that pill is a anti-backfire device. I have never serviced a stuck one, and that would be in
a completely neglected engine with no oil change for 2 years.
In carburetor engines, we would just clean the old metal ones in the part washer and reinstall.
The % of PCV as an inlet charge is very small. The constituents will be completely burnt in the combustion cycle.
Stuck rings are typically caused by low engine loading with brief and infrequent high loading, then and poorly formulated or expended oil.
Many engine designs have experimented with low tension ring designs that afford poor sealing.
If you DO have a hot stuck ring its likely #2 and #1; not the oil control which has generous ports for the clean filtered oil to cycle through.
I would call Honda Customer service and see what they can do for you. But in the mean time change oil brands and substitute a quart with one of higher grade. Likely may not work but worth a go and the engine will likely enjoy it,
The primary purpose of any PCV system is to recycle partially burnt gasoline & condensed water vapour, that can accumulate in sump oil. There's really no problem with this. The fuel burns cleanly, water leaves as steam & everything goes out the exhaust pipe. Job done. Sorted!
However the system was never designed to burn oil & therein lies the problem. Modern engines (especially GDIs) with low tension rings seem to dump more fuel into the sump (especially when it's cold outside). That fuel can only exit the crankcase one way; via the PCV valve & into the air intake. If you couple higher rates of fuel recycling with thinner & directionally more volatile engine oils, then you increase the rate of 'oil carry'. This is Boyle's Law & Charles's Law made manifest. If you've ever refined oil or designed crude distillation columns, you will grasp this in a heartbeat. If you haven't, it gets trickier to picture what's happening.
Yes, there's usually some kind of physical baffle system, designed to separate the bulk of the oil droplets from the gaseous blow-by & re-evaporated fuel/water. However any oil that has entered the vapour phase cannot be knocked-out by a physical baffle. If life was that easy, I could solve global warming at a stroke by pumping air through a physical baffle and sitting at the end of the baffle with a big bucket to collect all the carbon dioxide!
If the hot recycled oil actually stayed in the vapour phase, it might be easily to burn but it doesn't. As soon the gas stream traversing the PCV valve hits the cold intake air, the oil condenses back into liquid droplets which will resist complete burning. Not only that but the induced swirl inside the combustion chamber throws the droplets towards the bore (think of it as a centrifuge) where combustion is worst & where some gummy deposits inevitably end up getting caught up in the ring pack.
There are two distinct phases to this problem. Usually, in the first phase, oil consumption is tiny but significant. It may last 50,000 miles of engine operation. The build up of gunk in the oil control ring is slow but progressive. In this period, the oil control ring can still 'bounce back' despite the presence of large amounts of gunk in the groove.
But a point comes where the ring does get properly stuck in its groove & to all intents & purposes, that ring is effectively just part of the piston. Oil is thrown up or sprayed up under the piston crown but there in now no primary bulk oil scrape (sorry, can't think of a better way to describe the process). Now some of that 'unscraped oil' can find it's way up the side of the piston under hydraulic pressure supplied by the downward motion of the piston itself. It can now start traversing the 2nd & Top rings, most likely taking the line of least resistance through the ring gaps. Now the oil has a direct route to the combustion chamber. It's a bit like having a busted valve seal. From 50,000 miles onwards, you're likely to see a much higher rate of oil consumption because the oil loss is from underneath as as opposed to 'over the top'.
This may not make sense to you but it makes perfect sense to me & reflects much of the oil behaviour I'd repeatedly see running engine tests like the Sequence IIIG & Peugeot TU5.