Roy also used a bit more than what you mentioned. Yes, he did ream the barrels smaller than the sleeve diameters but he also "sweated" those liners in place by heating the barrel to expand its diameters and freezing the liner.
https://youtu.be/F5q5JqmFpHk?t=179
This is similar to the method he used.
Using heat and cold to expand and shrink the respective parts is not 'sweating' them. Sweating them is the use of solder.
In the case of a liner, that would involve pre-tinning both the bore and the liner with solder, then heating all to above the melting point of the solder, and sliding the parts together, all while juggling with enough additional solder to prevent leaving voids in the joint.
All of which usually takes a pretty good selection of extra hands, in a limited amount of space and time, to pull off, which is pretty much why so many guy went to Acraglass or similar 'glue' formulations to install them. Less swearing, fewer burns, more time to work.
I spent a LOT of time installing bushings in airplane parts with liquid nitrogen. Once the cold part touches the hot one, you have a very limited amount of actual time to work with, and you might just as well save yourself the effort, and press the parts together from the outset.
Cold shrinking large diameter bearings or bushings with Liquid Nitrogen isn't onerous, but the amount that a small diameter part actually changes size in a couple hundred degrees temperature change is pretty minor, and the heat transfer to the room temperature or 'hot' part once they make contact, is almost instantaneous, even if you manage to fit the small diameter part on to a larger mass and cool that too.
If you really want to know how close you have to work, look up the Coefficient of Expansion, multiply that by the number of degrees temperature change, then multiply in the diameter of the hole.
Better yet...COE of Steel 0.000012" per degree F, per inch of diameter.
Temperature of Liquid Nitrogen (colder than most folks have) is between -346°F and -320.44°F
Lets say room temperature as a good starting point. 75°F sounds about right for a round number.
Call it a half inch diameter liner. .22 rimfire liners are a bunch smaller, at 5/16 inch, or .3125", but lets use .5 for a nice round number.
So, .000012" x 405°F (splitting the difference between min and max LN2 temperatures, plus the room temperature above zero) x .5 = .00243 inches, or 2 1/2 thousandth of an inch.
At least, until the cold part touches the warm one, and the heat transfers over.
Oh yeah, if you want the thing to grip the bore, the bore has to be smaller than the liner starts out, at equal temps, so you have considerably less than that 2 1/2 thousandths to fit the liner in to while hoping it stays cold while you do it.
Which tends to make me believe the guy with the hydraulic press was likely on to something!

Like that pissing around heating and freezing skinny parts is pretty much just a waste of time, when you can press fit the parts and get a pretty reasonable interference fit.
My money is on that no matter how quick you were, you'd get about two inches of that liner in to the barrel before it locked up solid, if even that.