You'll definitely kill more with a shotgun. Bait & soft calling will get you a couple shots with a rifle around but action will be MUCH slower (verses hard calling/ run-gun). Another option is to set up in a field & call. Crows will investigate then fly off to the tallest tree other side of field & mock you. You'll make them smart, but get a few shots along the way. Don't carry the HMR though. When they light, it will be somewhere in the 300 yard range. Much closer & they'll opt to just keep going. Find a diff tree ~300 yards away & mock you...
Sometimes, your can soft call to get the crows coming & then hush you calls. Non-pressured crows sometimes loft in & land to scan the seen; in big woods or the like (they can see to good enough in a open already to need to scan much). Often you can get them to land in this situation but is seldom conducive for a clear lane of shooting.
Moral of the story, unless you've got a lot of time to shoot few crows... Carry a shotgun!