Hmmmmm, interesting topic, nice.
Have to say I don't know a slip hitch. Guess I'm not one to know all the 100s of different knots like a lot of you do. Use maybe 6-10 knots.
Now, if you don't have a break away lanyard for this situation and you use a lanyard anyway. I'm stating the obvious I guess but: in that situation, make sure you at least don't use a steel core lanyard.
The rope lanyards cut very easily and fast when under tension.
I had to do this many years ago when I just started climbing. Topping out and dropping some difficult trees for a logger. Tied in the top (big red oak), came down and when out on a big heavy lead with a lot of horizontal weight. Put my lanyard around the lead, (probably didn't need to), undercut or cut a tight notch. Then when I started cutting the back cut it started to go pre-maturely (of course). The holding wood was very thick and the limb naturally started to split down the middle (the part I'm spiked into and have my lanyard around), as the splitting yanks me up against the log I swipe the lanyard with the saw to cut it. Cut it like nothin'. Could have been bad if I had freaked out and didn't think fast.
now-a-days I would have bore-cut and I probably wouldn't have put the lanyard on in that situation.