Here's what I did:

1. Duplicated the Longbolt Missile weapon along with its actor and 3 effects
2. Duplicated the unit 'Weapon - Longbolt Missile' and its actor
3. Set the new unit to the duplicated weapon
4. Changed it so 3 missiles fire instead of 2
5. Changed the Mover of the unit to 'Drunken Missile'
6. Changed the damage and attack speed

Here's the result:


As you may be able to see, the missiles do damage as they hit the turret, but the (non-damaging) explosive effects happen right as the missiles are fired, instead of when the missiles make impact.

Haven't got a working data editor atm but I'll try remember what to do:

Search the actors for the one named something like Longbolt Missile Impact. Make sure that the weapon or unit is linked to that, and that the Longbolt Missle Impact actor is set so it explodes when the weapon finishes firing, or whatever.

Could be talking out of my behind as I can't check it with a data editor

Can't find any actor with the word impact in it relating to the weapon. :\ Get your data editor working so you can help me. D:

Reinstall or something. :\

The missile turret attack actor has this event

Effect.LongboltMissileU.Start
->At Caster
->FromEffectTreeDescendant
ActionImpact

When I remove it the missiles no longer explode on impact.

Well, that didn't help at all. But the good news is I found another weapon to replace that is more fitting, so it's no longer an issue.