If one is considering building a 338 Lapua Magnum on a CZ 550 Magnum action.
What caliber would be best for conversion. Thinking about feeding..

416 Rigby

As jwp475 says,

.416 Rigby is the natural choice, and I have done that, having a .338 LM made by re-barreling a CZ 550 Magnum .416 Rigby.
It fed well, and is currently awaiting re-barreling again to .500 Jeffery which it strangely enough is a flawless feeder of too.

But I have done other .338 LM wildcats with CZ 550 Magnum .458 WinMag rifles before I developed a full appreciation of that cartridge.
Requires the minor extra work of opening up the bolt face.

There are two factory boxes in the CZ 550 Magnum, made of sheet metal like in many other rifles.
They are marked either ".375 H&H" with ribs stamped in sides of box,
or ".458 W.M." with no ribs encroaching on the internal width of the box.
I have found either box in .416 Rigby CZ 550 Magnums I have owned,
as from the factory, no rhyme or reason.
I think the .458 W.M. stamped boxes work better in the .416 Rigby.
My slickest feeding one had one, held 4 down in .416 Rigby or .338 LM.
With the .375 H&H box it might hold only 3 down.

Try your candidate rifle with feed dummies before deciding.
Even a most common .375 H&H might work well.

More fun to be had are the barrel specs for length, contour and twist to be used,
fluted or nonfluted, braked or not, iron-sighted or not, stainless or chromoly, wood or synthetic,
sporty hunter or heavy sniper ?

I have also done .338 Lapua Magnum wildcats and proprietary neckings (.308, .375, .395, .408, .423, .458, .500 and .510 calibers)
on several CZ 550 Magnums and BRNO ZKK-602 (.375 H&H, .416 Rigby, .458 WM/Lott),
an FN Mauser .30-06 and Wiebe bottom metal for .500 Jeffery allowing 3.5" inside box length,
a Winchester M70 Classic .300 RUM action with Sunny Hill drop floor plate and McMillan stock, limited to just a little over 3.6" inside box length,
a Weatherby Mark V .30-378 WbyMag with drop floor plate capable of 3.8",
and a Dakota M76 African .416 Rigby action capable of 3.8", like the CZ 550 Magnum.

338 RUM perhaps?

Yes or 338 Edge which is basically the 300 RUM necked up. Same capacity, 338 Edge might be a grain or two bigger than the 338 Lapua. Personally I reckon if you are going to have the issues of brass cost and the Rigby size case rim then the 338/378 is the way to go and you get the big case capacity. Asa bonus if the 338/378 brass is not available making it from 30/378 or the 378 is real easy and simple.

What a relief ! Sir Mike is alive !

And Ron I have had two doses of the vaccine. !!!!

I built my custom 338-416 Rigby Improved on a CZ550 Safari Magnum action that started out in 416 Rigby. It works flawlessly and is extremely accurate. No mods were needed.

Cheers.