There was an issue focused just on their downtime after the first encounter with The Red Skull; there was a downtime issue after the overlong Apocalypse Twins storyline. So if comic book time is something that needed to be available to them in order to draft a new teammate then it was shown that they had it.
And as for candidates...neither Rachel or Psylocke are down with Cyclops like that to the point they'd not join the Unity Team because of loyalty to him. Hell, Rachel works at Wolverine's school!
M could have been brought in.
Mantis and Moondragon aren't in the Guardians anymore so if Cap/Iron Man could get Capt. Universe on the Avengers I think it should be easy getting a hold of either of them.
Sage
Mimic
Devil Slayer
Sersi
Aarkus (The WW2 Vision who was in the Invaders with Cap)
All available if Remender had just decided to fix what is a glaring flaw in the make up of this team.
Psylocke in the very first issue of Uncanny X-Force literally said "fukk the Avengers", she ain't helping
Rachel Summers, as AvX showed, is more loyal to Cyclops than Logan and doesn't take kindly to the Avengers as experienced in the Avengers/X-Men battle where she owned Cap and Thor
M doesn't fukk with the Avengers either and is/was being used in X-Factor
Moondragon is dead according to her last appearance in Guardians IIRC, don't even think Mantis is currently in the 616 Universe
Sage, loyal to the X-Men first and was being used in X-treme X-Men
Mimic - A Villian
Devil Slayer - Come on
Sersi - The only good option, but she ain't been an Avenger since Black Knight refused to give her dikk
Aarkus - Wasn't his body scrapped?
Look, at this point you are throwing names at the wall because ALL of these characters would lose to the power of Xavier anyway. But I AGREE with you that Cap SHOULD HAVE seeked a psychic, but Cap has a thing about psychics as he has never seen the value in having one. Every Cap lead team of Avengers has never had anyone with a dedicated role as a psychic. To Cap, explaining to him the value of a psychic is trying to teach an old man the value of Twitter, lol.
Psychics have always been an X-Men thing and a GLARING flaw in Avengers rosters. I HOPE after all this AXIS stuff is over, Cap will smarten up about this.