2006 is a great year to pick from. As has already been mentioned, I would be very in for a Grizzly Bear, Yeah Yeah Yeahs, Joanna Newsom, Whitest Boy Alive, or Hold Steady ROTM.
It's too bad they've already done Hot Chip, because "The Warning" NEEDS a reissue badly.
A few other ideas to throw in the mix:
Ghostface Killah - "Fishscale" (Probably the only rap album from this year that would be large enough to go Essentials as opposed to RHH, and desperately in need of a reissue)
Cat Power - "The Greatest" (They've done some stuff with Matador in the past, last pressing was 8 years ago)
Belle & Sebastian - "The Life Pursuit" (Another Matador option, had a 2014 reissue so perhaps less likely)
Camera Obscura - "Let's Get Out Of This Country" (Great album from a somewhat-forgotten former indie darling, might not be a large enough draw)
Sunset Rubdown - "Shut Up I Am Dreaming" (This is an interesting option, as it has never been available on vinyl, don't know if Jagjaguwar has the rights to this like later Sunset Rubdown albums....)
Junior Boys - "In The Morning" (Electronic ROTMs are few and far between, but this is a solid candidate...hasn't has any reissue since it first was released)
Lily Allen - "Alright, Still" (I don't see this as a great possibility, as they don't normally go too full-on pop music, but this album holds up pretty well)
The Pipettes - "We Are The Pipettes" (OK, this is a total flyer and absolutely a "homer" pick as I love this album and wish more people knew about it)