I am pretty convinced that the best Spellslinger is actually a Gunslinger1/Wizard6/Eldritch Knight10, so this topic is germaine to my interest.
I really don't think that the Grit Feats are particularly appealing, but, by the same token, offering the choice to the player is hardly overpowering.
With regard to diverse training, would an Gunslinger/Eldritch Knight automatically get ALL of the deeds available to a Gunslinger of equal effective level? Would my build above automatically have access to all 11th level deeds? This does increase the power of the build. Deadshot and Targeting are my specific concerns. Both, if read liberally, are powerful, and giving them to a Spellslinger really steals the Gunslinger's "thunder," if you will.