Besides the obvious 6 level slide into Arcane Aecher, like it was meant to be... I have been looking at the Arcane Archer weapon proficiencies, and how you now qualify for Eldritch Knight...
Arrowsong Minstrel 6/
Arcane Archer 10/
Eldritch Knight 4
BAB +18
Base Saves +9/+11/+9
CL 16
Arrowsong Minstrel 6/
Arcane Archer 4/
Eldritch Knight 10
BAB +18
Base Saves +9/+10/+9
CL 18
As you can see, Eldritch Knight brings a higher caster level, which DOES seem important when, literally, the whole trick is putting spells on arrows... if the spell doesn't do SOMETHING, the trick is wasted, entirely...
Now, Arrowsong Minstrel 10/
Arcane Archer 10 ends with
BAB +17
Base Saves +8/+12/+10
CL 17
So, you have "choices"... are the toys given by Arcane Archer worth the drop in caster level? Are the Bonus Feats and caster level worth the lack of Enhanced Arrows, and other Arcane Archer tricks? Are extra levels of Bard worth it past 6, at all?
It depends on what you want out of the character. My own Arrowsong Minstrel is staying pure Bard with a single level of Fighter. I want the extra spells and performances that Bard gives rather than some arrow tricks.
Bard 7 gets a performance up as a move action. Inspire courage improves with bard level, and there's other odd things which improve with bard level. Arcane archer or eldritch knight aren't essential to a bard archer at all - AA 2 gets you confusion spells at longbow range, but that's as much as I'd dip out of the class, and only if I was in a game where that range seemed likely to be useful often.