I don't know what pressures the 22 Spitfire runs at, but the Marlin 62s came from the factory with pinned, rather than threaded and screwed in, barrels, so I'd think that you'd have to watch the pressure if your new barrel is also pinned.
I have a Marlin 62 that has been rebarrel, properly threaded into the receiver this time, in 218 Bee and it works fine within the capabilities of the 218 Bee's case capacity and brass thickness. 218 Bee brass from Winchester/Olin isn't what I'd call "overly robust" and if I try to hot rod it, case life is limited to 2 or 3 cycles.
I have owned 5 or 6 of them, 3 or 4 in 256 and 2 in 30 Carbine. I thought that the actions cycle smoothly, but the lever is very narrow and tends to "bite" the shooter's hand if you cycle the action rapidly. I have also had to reinlet the stocks on all of them to get the safety to function reliably. Accuracy with the 256 was better with Winchester/Olin 60 grain HPs and with the 86 grain Remington 25-20 bullets that I use in my reloads, 1 to 1.5 MOA at 100 yards with a 2-7x mounted. I never worked up a load for the 62s in 30 Carbine, but they shot Remington 110 grain factory ammo into 2 or 3 MOA at 100 yards with a 1.5-4.5x scope mounted.
I always thought that Marlin missed the boat on the 62s by not making them in 44 Rem Mag. It seems to me that a 62 with a 20" barrel in 44 Rem Mag would have been a dandy little woods rifle for shooting whitetails and such.