Players in AO Q R3 aren't allowed to play in Sheffield qualies, right?
I think they can play in both. They only have to withdraw if they make the main draw of the US Open.
I was looking at last years US Open and corresponding Challenger #35a Como.
The following players lost in Q R3 US Open and played in Q 1R Como
For Q 3R losers, if they go for LL spot, they have to withdraw from challenger. Once the Challenger draw is made, once a player sends picks, he/she can no longer apply of LL of the grand slam.