Often there is enough "free play" in the PEX tubing attached to the anti-siphon valve that you can push them down toward the basement and gain several inches of working room. On my trailer, I can push it down, almost 8", enough to get the actual valve completely clear of the sink basin.
If you play around with it a bit, you should find that it's not as difficult as having to pull the sink to access the anti-siphon valve.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS