Sounds like the Seafoam is getting a bite on the gunky engine deposits. So continuing that process is a good thing.
The thing about the ring problem is that there may not be enough oil drain holes in the 3rd (bottom) ring set, which are oil control scrapers. So what happens is, the oil "cokes" up, forming carbon deposits on the scraper rings and they can't do their job. In fact more oil is going past the rings and being burnt in the combustion process.
This problem can happen even in the later engines with improved oiling design, if the EGR system was abused or not functioning properly. Exhaust Gas Recirculation does cool the combustion chamber, so if the EGR valve & its control system aren't working right, or the EGR/passages are plugged the pistons are gonna run hotter, and this can lead to oil coking. Also check the PCV valve, if it's clogged it can cause oiling problems too.
The oil control (scraper) rings are suppose to pull down any excess oil on the cylinder walls, on the piston downstroke. So, the cylinder walls should be receiving adequate lubrication, the real problem is the oil is not being "scavenged" back into the crankcase.
Piston slap can be caused by many things but typically it's either mfr's piston-to-cyl tolerances, or extreme wear. Aggravated by the use of longer-throws on the crankshaft and really short "slipper" piston skirts. GM had such a problem with their 60-deg FWD V6's that they had to go with Teflon-coated pistons, running at extremely tight tolerances, to fix the issue.
When I rebuild a 2.8 into a "3.2 Stroker", the aftermarket pistons I used had the Teflon coating on the skirts. And specific instructions for the machine shop about the tight tolerances for boring & finish-honing the cylinder. It was a very tight engine and even after 10+ years it's running very well in the hands of my Nephew.
At any rate, what you're doing may be working, hopefully you'll be seeing an improvement in oil consumption. I would also be using the Gumout Regane fuel additive, to attack the problem from that end as well. You may find that using Gumout along with the Seafoam oil treatment, your oil consumption numbers may improve to where you don't need to do the Seafoam cylinder-soak.
I'd use the Gumout Hi-miles stuff as it has a small amount of top-end lubricant and that can't hurt a bit. Far as the piston slap goes, as long as it's going away when the engine's fully warmed, not as much of a concern. Especially if you start seeing an improvement in oil burning.
You could do a "shock" treatment with 2 bottles of Regane, with a one-bottle followup: https://www.walmart.com/ip/16888905
Geoff did the carbon-cleaning regimen on his Rav4 and noted an improvement in oil useage, so there's some good anecdotal evidence that the process can work.