A Meopta made Zeiss Conquest MC scope will mount without extension rings and have more than enough eye relief on a No.1 for anybody built to non-sideshow dimensions. For a .375 Tropical I would look for a 1.8-5.5x38mm or 2.5-8x32mm. They have a ton of eye relief that is nearly constant thru the power range. I want to say it’s 4” but it may be slightly more. Just as important for No.1 usage the have a rather long tube length. It might be hard to track one of those two down but the 3-9x40mm work just as well, have the same eye relief, generous tube length and are easy enough to find. I wouldn’t sneeze at the 4x32mm if you come upon one. I’ve one on a 45/70 and it’s quite a handy rig in the field.
Unless you require a 12” length of pull on a bolt action you will be perfectly served with a Conquest MC on a No.1