I have a 22LR CZ455 in the Manners stock, Lilja match barrel, Timney trigger, Vortex Viper 4-16 PST that I frequently shoot out past 200, 250 yards with. It will hold >1 inch 5 shot groups at 100 yards for 5 groupings as a warmup, and then I start shooting steel rounds or polymer squares at further distances.

There are a ton of posts/pictures of these in the 22LR Rimfire section on SnipersHide; I'm TheGerman incase you are over there as well.

The 22LR is really limited by its ammo. Even the Lapua Center X or Midas I use can have muzzle velocities that are 50fps from shot to shot. While this isn't very evident at 100, at 270 like I was shooting today, sometimes you can make 4/5 hits on a 4 inch cube like I did today and then the next 3 rounds all fly 6+ inches over the target. This is all from the ammo, and can easily be seen if you put a cardboard box behind the target; it looks like you are shooting a ladder test where they are all perfectly vertically strung.

So what I am questioning is, most people use the 22LR to plink or shoot for accuracy at 50 and 100. I know I am taking it out of its comfort zone at 250+ yet have a lot of success. However, being limited by the ammo, would 22 WMR be better for what I am doing?

From my little bit of research the 22 WMR has higher velocity (22LR Lapua is 1060 vs Super X is 1910), roughly the same cost as Lapua Center X/Midas as well as has an actual metal jacket.

Am I missing out, or is again, the spreads in FPS on the ammo the limiting factor?

I had the same thoughts as you with the limitations of 22LR and went for a Ruger American in 22WMR.
I don't have many rounds through it yet. Groups at 100 seem to be hit or miss, still experimenting with ammo brands.

Have taken it to 200 yards with good success. Will go for more distance soon.

Honestly if go with the .17 if you want to stretch further. I have very limited experience with the WMR but the experience I have was pretty spotty accuracy wise.

Same sort of issue you are seeing, huge velocity swings shot to shot

.22 wmr ammo is too expensive and hard to find.

.22 LR loaded with Stingers or something similar is a better option.

Stingers in my 10/22 are more accurate than standard MiniMags. I dont shoot them much though, regular cheap Federal 525 Value Pack 36gr. CPHP @1260 MV are reliable and super accurate for me, but ive never tried shooting as far as you. I wont shoot Rem .22lr anymore because you can hear the difference from round to round and they dont cycle my autos. I have problems with duds using Win .22's in my autos, a bolt action and a revolver so i dont buy them anymore.  A friend of mine shoots Geco, Ely and even Blazer .22lr ammo at 100 plus regularly and says he likes them a lot. He shoots 8-12" steel plates though, not shooting for groups. I dont know anyone with a chronograph to give you any actual velocity/spread data.

Edit: I know a guy who "snipes" vermin on his property out to 250 yrds with his .17 all the time, says he loves the round. I dont know the rifle model but he shoots Hornady V-max ammo.