Re: Which Base? 20,30,45 MOA?
Since it has the TMR reticle and it is FFP, I would probably opt for the 30MOA with a 200-300yd zero which will get you out further in terms of max range of internal adjustment with the scope. Since you [hopefully] won't be shooting it at distances shorter than 300yds or so anyway, it isn't a huge issue to hold under for those few instances where you may need to take a shorter-range shot.
Like folks have said already...if it were me and I were trying to stretch out the legs on a 338LM, I would sell off the Mk4 and buy something else, whether it is the new 5-20x SS or something else. With 30mils on the SWFA SS 5-20x (roughly 103MOA), you could easily get into a 30MOA or a 45MOA canted rail, still get a shorter-range zero and still reach the extreme end of the 338LM with the scope's internal adjustments. Same thing for a scope like the NF NXS F1 (or even a 5.5-22x non-F1 if you want to sacrifice FFP) will have a TON more adjustment range at roughly 40-50MOA MORE internal adjustment than the Leupy.