YW.
Here is a little bit of controversy... Rings spin in their grooves. If rings spin, then the thrust fallacy is evident as to how does the ring get away with spinning were the stagger is not? In other words, this thrusting up and down has yet to hurt an engine's integrity as if it will blow smoke, the rings will move away from each other within a few hundred miles; installed another way.
With that said, I collect all my gaps and run them in the back. I can tilt on the piston's pin, watch the cylinder capture each ring, were I have to look 120° off of each one, making sure it does not fall out of it's ring groove. I watch all 3 at the same time are the closing, or the narrowing of the ring's gap into its individual groove.
By setting the round sides in the bore first, I can rock the barrel to circle around the rings, or pop one in at a time, straighten the barrel over the middle ring, then push the round up into the barrel with a slight cock, but not enough to pop out the compression ring; I have to start all over.
With rings and bore, you can cock or drop. Either way. With lube, I coat the skirts only. Whatever is left on my hands, I wipe the rings so that is the lube for; I do not oil my barrels. Those are left dry. The skirts are my only concern. By the time that crank comes around, it whipped oil up the pistons so it's really a waste to lube anything else... Sans the wrist pin and all that.
Open end of the piston pin's C clip; has the open gap facing up. If they are spring clips needing a collapsing tool to close the gap down meeting the pin's groove. There is a flat side to the clip. That flat faces you. The round side can be pushed by the thrust of the pin. So, that cut is how you dig into the groove, not pop out of the groove.
If those rings are too hard on the fingernails, because I do not use anything else to push the rings in... Sans a nylon type of stick to push on that brittle ring. Unless, these are really hard to push in? Then I use spring steel over the rings. Like some windup toy, that spring needs to be wide enough to cover over all 3 rings. Then, a hose clamp claps over the spring steel. This protects the skirts from being cut by the threads made for that hose clamp; not to screw down onto the soft piston material. Ideally, the narrower the spring steel the better.
You lower the clamp so the thinner spring steel sticks up and out from the clamp. The taper of the bottom of the barrel is for ring collapse. That thinner starter spring, being [slightly] above the compression ring is, how you make the rings all enter with ease. Just a suggestion, moving 180° away from the 120 degrees spread of old.