i use sling/krab sets; occasionally half hitches instead. But; i always dog the half hitch into the keeper of a branch crotch or imperfection.
Usually i cut the bottom limb first. Sometimes i'll place sling around bottom limb and on harder limb over it. Then jsut tie rig line further out on harder limb; tension rig line well. Cut lower limb to give more weight at whatever distance from/behind rigging line hitch on harder/2nd limb. This, gives more leveraged ballast on stob end to keep green end up higher/ give more float; especially when swing it around, and trying to keep it high enough to sweep out from over obstachle below.
Another technique, is to run rig line more horizontal, to try to get limb over roof to sweep off sideways. If that seems chancey/ might not come sideways enough before tipping down you can try ballast technique above; but what if no limb under to cut first for more ballast? Then, i really tighten line well; and find another limb along the way between rigging point and tricky load to move sideways off roof etc. i place sling on the 2nd/helper limb and clip to rig line near center of trickier load (ast end of rig) and rig point or so. Then give face to trickier limb; and back cut almost to failure. Quickly remove saw and go to 2nd/helper limb (that can be partially pre-cut too); and quickly cut it off; slamming it into tighened horizontal line to leverage line hard. This multiplies the sidewards pull of the rig line on the trickier limb, to hopefully flex it's hinge and pull it around sideways (if precut right).
If i can't get a near horizontal run from rig point to end of line/trickier limb; A) the leveraged force willnot be as much B) the helper limb may run down to the trickier limb and possibly make things worse. So then i place butterfly at about halfway point between rig point and trickier limb. Also pretighten rig line even harder, possibly heavier helper limb. For the leverge multiplier is going to Horizontal angle X line tension X helper weight. As i give up some horizontal angle; i logically have to increase line tension or load wieght multipliers for same effect.
This works on perpendicular force applied to a tight line to leverage line to higher tension. So, jsut as i may use a zrig as a tie down; i will only use that to stiffen line/ to make it resist bending(resistance to bending gives leverage when perpendicualr/ non-inline is applied). Then bend lines of z, to get my real/ high leveraged tightening. i use this to pretighten the line (tighten with inline force, then Brion Toss's line sweating descriptions to tighten more) in pretensioning; then hit that tighter line with horizontal force from helper limb.