Oldtimr and Topgun kinda poked at this, but I'll flat ask the question - do you have handgunning experience to suggest that it's not the shooter? Have you ever shot better groups out of a handgun, or is this your first date? 6" groups at 15yrds can be asking a lot for a new shooter.

Improper timing is different than misalignment, and neither can get disregarded, because even though Ruger does make great stuff, lots of folks modify them on their own, and lots of folks run them until the wheels fall off, AND quality control issues DO make it out the door sometimes.

If a revolver is out of time, then a new cylinder CAN sometimes fix it if the timing issue is from a galled/worn/peened indexing ratchet on the cylinder. If it's out of time because the pawl is worn/peened/broken, then a new cylinder will not fix that. The pawl happens more often. Improper timing is a problem if it's too slow at the front end - meaning the hammer is trying to move the cylinder while it is still locked, or too late at the back end, meaning the cylinder does not lock before the single action sear engages, so the cylinder is free spinning when the shot is fired, which can allow for misalignment. Unlocking too early or locking too early is rarely an issue. Timing is VERY easy to check - draw the hammer rearward, if it locks up before the hammer engages the sear or exactly at the same moment, then it's properly timed. Any revolver, even a Ruger, is vulnerable to timing issues, and even normal use will create wear that will eventually slow them down and cause issues. Fast firing, fanning, or even just bad technique of cocking the hammer too fast will accelerate that wear.

If a revolver chambers are misaligned from the bore - which RARELY happens for a Ruger, even if you swap cylinders between two specimen, BUT IT DOES HAPPEN - then it's just plain not safe. This is easily checked with a modified range rod (can't just use a bore sized rod). When the cylinder is locked up, the chambers should be concentric for the forcing cone, or at LEAST the bore of the throat and the forcing cone must be tangential so that the bullet can do its job and forcefully line them up without shaving part of the bullet. Any smith should have a modified range rod to check this. The brownells range rods don't actually work for this purpose without being modified, since they are fit to the bore diameter, and the forcing cone and chamber throat should be larger diameter.

Recovering some un-damaged bullets would let you know a bit more about the misalignment issue.

But... Improper timing is super easy to check, and will only affect accuracy if it isn't locking up prior to the shot and the revolver is firing when misaligned. Misaligned chambers, whether unlocked or incorrectly machined, will affect accuracy by 'shaving' or 'squishing' one side of the bullet. You'll see this in recovered bullets and by excessive leading in the forcing cone, and even by torching in the barrel from mal-formed bullets letting gasses blow by.

How does your forcing cone look? Is the tennon torched? Is the forcing cone pitted, scorched, or leaded?

How are the chamber throats? Can you 'dip' an unfired bullet into the mouth of the chamber (from the wrong end) or does it not fit?

Is there any torch pitting in the bore (usually happens as a streak or a ring)?

How are the cylinder locking notches?

How much rotational shake do you have at lock-up?

Have you tried any different ammo?

The good news is this:

RUGER WILL FIX IT! They carry a lifetime warranty, and if it's shooting that poorly, they'll fix it.

EDIT: Those two new cylinders may not fit safely and you either need to go through the motion to ensure that you have proper alignment, or pay a smith to do so. Most Ruger cylinders drop in within spec, BUT, if you have an issue with your cylinder, it's more likely that you have an issue with your GUN so the new cylinders will have the same problem. You NEED to confirm headspace, bore alignment, b/c gap, and endshake before you put a single round into those, unless you want to run the risk of losing some fingers.