My understanding is that the suppression itself doesn't come from the direct hit, it comes from the tethers that come out a second later. I did the same thing, and a friend pointed out that the suppression did kick in shortly after I died. Still annoying though - I think a direct hit should kill in one. From now on I try to tackle them indirectly instead.

Not sure, I'll test this if I can, but another guy says the suppression effect happens during the second shot when using quiver.

All three arrows can ohk, and tether after a small delay. Sunbreaker will survive the first shot, so you have to hit them again.