Exactly re: the eyelets at the gate...Looks like a single tie down through the carry handle on the eyelets at the tailgate would secure it well!
I have a 10'10" inflatable SUP but I have not tried transporting it inflated yet. It would need the tailgate down or a bed extender. Instead I got a valve adapter to use a Schrader valve on the SUP to fill to 15 psi via my Viair compressor I already keep in the truck for off road and emergency. That and a cheap air mattress 12v pump to deflate it, it's not bad to inflate and deflate but definitely not as nice as strapping it on filled.
I also have a portable air compressor and valving. For short trips, not freeway, this works but if you are doing long haul then deflate and pack into the bag or fold into the bed. That looks like a beautiful area to paddle at.