That's a heckuva rundown by Hank & Chasing_smoke .............
Jimmy, James & GC have some good angles on this too !!!
I would agree w/ Chasing_smoke......looks like eye of round........different possible approach here......
I would marinate them while other things were going on (family event) then very quick sear, then away from the coals indirect for a short time.......
the reasoning being: a piece like that doesn't have much fat, the marinade 'replaces' or 'fixes' that somewhat......the sear 1st, in that case, does seal in what moisture has been added & the indirect helps let them finish
gently.........
Cleaned out the freezer a couple years ago.......all the 'mystery meats'....pork chops, eye of rounds, country style ribs, on sale stuff that somehow got buried........ threw them all in a mixed up marinade concoction for a day & a half............. smoked them all on one kettle, two levels full of stuff @275~300 for what seemed like not a very long time.........these were destined to be chunked up small for adding to pans of beans................several of these pieces, notably the center cut chops (pork version of this kind of steak above ) was possibly the best, most tender I've EVER done..........can't say enough for indirect grilling / smoking..............
If there's one thing I have trouble with, it't not overdoing stuff like steaks, lamb chops and salmon, all of which I prefer on the rare side (and all of which I frequently overcook.) I feel your pain!
I have these troubles too.....at the higher heats.....but tend to 'under-do' stuff like lamb chops & some kinds of steaks......