Mike, personally I'd go with the L5W 8/12 on your Burkie. It could be different if you were looking at matching a new reel with two or more rods, then the bit heavier H5D might make more sense. My L5W sees use on various mid length rods and seems great match. Specific, and similar to yours a Scott ARC 12'8" 7wt ..which is a solid 7.5 line class any day. Just checked, it's scripted at 7.9 ounce.
I don't know how much backing I loaded to spools but it was a slug (from bulk) Going to say you won't have trouble getting 200 yds. I've had my original RIO integrated 'Beer Can' 550gr on one, so with finer run line your golden there. I can take picture of spools if you'd like to see backing depth. They are big game saltwater drags. The original (LW and HD) drags were fantastic.. with the later up-dated L5 and H5 version reels they are phenomenal! No worries on that front.. Outgoing click is machine like, kind of subdued but plenty audible. They tick like a Swiss watch and have very solid well built vibe to them. Full frame, so no worries about running line jumping ship.
If I were forced (nightmare!) to pare the reels down to one single manufacturer for all fishing fronts my Danielssons would still be with me when the dust settled.