Hey Frank - the .375 Rimmed is a worthwile chambering for the #4 or #3, imho.
A slightly more powerful chambering would be the .375 JDJ(IIRC) using the .444 Marlin case.

However, the .375 Rimmed would be fine. When Ken Waters did this chamber on a Ruger #1(or was it a #3Ruger?) he didn't load it very high, pressure wise, as was his usual trait.

Suffice to say, in either of the Enfields, it should do at or over 2,100fps with 270's, about the same power that the 9.5x57 was loaded to, factory wise.

You will have to work on the magazine tabs due to the larger bullet diameter. Converting it to a single stack, with Delrin slabs inside, screwed from the outside, might be an idea. The screws will have to be wood-type screws with beveled heads countersunk into the mag side - V-small dia. would work, I am sure.

I see you are looking at cast bullets. A 300gr. would be super and should get anywhere up to 2,000fps with appropriate loads.

From NOE, the 284gr. and 270gr. looks great.
http://noebulletmolds.com/NV/index.php?cPath=52&osCsid=qj89p0h1of7uqibrtlq9adnvd0

Buffalo Arms also has some nice moulds.
https://www.buffaloarms.com/bullet-moulds/buffalo-arms-bullet-moulds?p=3

On top of those, the RCBS 250gr. is also a good one and shot well for me, in my .375/06IMP & .375 H&H.
http://rcbs.com/Products/Bullet-Casting/Bullet-Moulds/Rifle/Bullet-Mould-37-250-FN-570.aspx