Your combo would say stay with distance like an enchanter. Bards are best with melee in my opinion. But the utility of an enchanter will benefit your casters better than a bard. The upside to a bard if you wanted to use one is the high regen and procs that can be used for both sides the melee and caster. If you use the necro's mind extraction lines even an enchanters buffs are negated. I side with Sic though for the enchanter, the twin cast and proc cast based dps bonus plus mana regen and CC will benefit the group dps the most.
Enchanter. I would also replace a necro with either another mage or a wizard. Necro is great for soloing but doesn't really shine in a full group (at least not until they revamp dots which may never happen considering it's been 3+ years since they originally announced dot changes).
I've never seen a reason to have both an enchanter and a bard. But I believe enchanter would be the route to go in this case.
A shaman can do well for a few added benefits of emergency heals, as well as some hp buffing. Obviously being this is a caster heavy group you'd be able to do a fair amount of dmg via spells. I see no reason to get rid of the shaman in place of a bard if you're already filling the last slot with an enchanter. Essentially all the things the bard can do are mostly negated by the presence of another caster in the group, but the pure caster can do it better. So no reason for that replacement. If you get the enchanter, you wouldn't need slows from the shaman and you could try out an additional pure caster, such as a wizard, which would allow for ports adding to the groups overall mobility. But that's only if you'd consider replacing the shaman, otherwise it's not a bad setup if you add in that crowd control / buffs /dots from enchanter.
I was thinking more that all a shaman does basically is heal and lay down med-high moderate dps (in a caster group.) It would make more sense to have another wiz or mage providing high dps. If Heals are the issue, then a druid, because they can heal, dps, and they offer some caster bonus debuffs I believe? I didn't list bard first because of desirably, but simply because I thought of it first. I don't know how well bard caster dps stacks with chanter caster dps buffs. Bards do have the ability to pull far better than chanters though. I've been a chanter whore my most of my life, it's only been the past month or so I've been using a bard, and only the past few weeks I've dropped the chanter for a beastlord unless it's mez heavy.
This is my understanding of various utility classes (Please correct me.) If I have played this classes its only been as a box, so most of my info is from that, or reading what I can, and much of it may be dated from 7+ years ago
Shaman: melee dmg bonus, strong group heals, weaker single target heals, cures, moderate dps mostly due to dots., moderate CC ability, ability to rez, HP (ac?) buffs.
Druid: Caster dps bonus (though weakened recently?) strong single heals, weak to no group heals, cures, moderate dps, ability to rez, transportation. I haven't leveled my druid, so I much of my recent info is things I've read, the rest is from before I retired and regularly grouped with a couple of druids. I'm waiting for the next double exp before I PL my druid and ranger, unless I get bored.
Bard: caster and melee dps bonus (though better for melee?) Pulling, CC, mana regen, slows, I've seen llow moderate dps with strong gear but mine puts out low (under 70k) dps. (lots more I simply don't know, the class is a complete mystery to me though I'm slowly learning.)
Enchanter: High caster dps bonus, strong CC, slows, mana regen, low moderate dps.
Beastlord: Melee dps bonus, hp buffs, slows, can tank or pet tank, minor heals, moderate dps.