I've had two blue grouse fly off with my arrow sticking out of them on both sides using plain field points. I recovered one but one was never found.
I too am reluctant to shoot broadheads into trees. They may stick there and be impossible to recover. Worse yet, as happened to me, I shot at a blue grouse on a limb straight above me in a big cottonwood tree. Perfect shot! But, the arrow kept right on going and I suddenly realized that it was going to come down eventually. I jammed myself up against the trunk of that cottonwood and hugged it till I heard the arrow stick in the ground about 20 feet away.
Now, if I'm going to use field points, I do a small modification as follows.
Get some smallish to mediumish finishing nails and a drill just a hair larger in diameter. With the point mounted on the arrow, drill a hole straight across and through. Insert the finishing nail and cut it off with about a 3/8" sticking out on each side. Bend each side back just enough to keep it from falling out of the hole.
It works on glue ons and with inserts or screw ins. If you are going to do it with inserts, use the aluminum ones for ease of drilling.
Tried, true and field tested on grouse, squirrel and bunnies.