If you have to / want to use that type of rifle for Zoot wshooting, I'd go with the 35Win SL. The balistics wil be much more friendly, but I don't think you'll find 10 round magazines for it.
I have a M1907 and frankly, I don't see it becomming a competition gun for the following reasons. 1. The ammo is very expensive and hard to get, so are the loading components. 2. The currently made 10 round after market mags are not very reliable, and thier expensive, about $50 bucks with shipping, when you find them. Original 10 rounders run $175 to $200 gunbroker. 3. The gun is a pain to disassemble (front sight must be removed). 4. Very, very, difficult to reasemble, due to the strong recoil spring. 5. The forearms usually break and crack and are difficult to fix in a lasting way. 6. Gun has a heavy triger pull. 7. The gun needs full power loads to function reliably.
the 1907 Winchester is a fun and neat historical rifle but it requires a lot of effort and expense to get running.
The best gun to get is the Thompson, 20 and 30 round magazines are easy to get and high quality. 45 ACP is a great carbine caliber, much less expensive than 351 Win. 45 ACP balistics are perfect for Zoot shooting. The Thompson is more expensive up front but you'll save money and effort in the long run. Plus the same 45 ACP round can be used for pistols, simplyfying things.
There are other guns, such as an M1 carbine with heavier lead bullet loads, might get under the velocity max. I have a Suomi M31 which will function with 9mm lead bullet ammo. I does not look very 'gangster' though.