37 yd quartering toward you shot,

Only YOU know your skill level, how accurate you are in a hunting situation. That's a good deal different than off of sand bags & target bench.

My bow is a Scorpyd 165, 105 fps faster, but no chance I'd take that shot. At 17 yds,......perhaps, I'd have to be there, but no way at 37.

And if this is from a tree stand like your second part of this question, then I do not believe anyone should take such a shot. That's a tough shot at anything over 20 yds at ground level for most, and just a plain no way if in a elevated location. 15-20'+ elevation even at shorter 14-18yds, is just wrong. The angle change to the shot makes a already hard shot a NO shot.

45 yrd. shot

If you have a chance at this buck while broadside or slightly quartering away, I'd take that shot. Your bow is plenty strong enough to give a full pass through at that range. And the farther away from you the deer is, the lower the chance/odds of a instant reaction (dropping to load his legs "jump the string").

Once again however YOU are the only one who knows just how accurate you are at that distance from a tree stand. If you've any doubts, put up a stand in your back yard & practice that shot in any & all conditions you'd be hunting in. Practice making full use of your sling & your stands shooting rail. Should not take long for you to be sure you can nail him at that distance if you've doubts right now.

EDIT:
I'd also look for a different & closer tree. A buck like the one you describe is one worth making adjustments to your set up for.

It sounds like you've some nice sized animals where you hunt. Given a bit more time you'll get some of them.

Best of luck!