Because the armor is so miserably thin, a turreted version would probably either be filled with LRM/5s instead of the bigger launchers, or else drop down even further to a couple of LRM/15s. That gets you fully 5 tons for LRM ammo, so you can feel more than comfortable bringing specialty ammo without compromising your killing power at all. You can bump armor to 5.5 tons, which is reasonably stout, and cram a vehicle flamer to set fires behind you as you retreat. At that point though it's an entirely different tank. Not really a 'carrier' any more in terms of throw weight or other features.
See, I'm on the opposite side of this.
Carriers aren't Tanks. They generally lack armor & ammo.
Thin Armor? Its a half ton less than standard carriers at 10 tons smaller chassis. I'd say it fits right into the norm.
Also, a Hover is just asking to get Mobility Killed before breaching the Armor.
They need to get in, deliver a couple tons of ammo on the enemy, and then get out.
The baseline Missile Carriers had 4 tons of ammo.
I don't see any reason to have more than that & with less total missiles, I'm fine w/ 3 tons max.
Specialty ammo? It's an Introtech design from the 3rd SW. Is there some out there? Sure, but not much.
Heck, I'd go so far as to say 2 tons Ammo & 1 more ton of Armor. That covers the 5th location of Turret.
As Devian noted, you need LRM20 to clear mines & it's the only single launcher w/ the potential to force a PSR even if it is on an 11+.
They way I see your design is essentially a "Rocket Launcher Carrier" only w/o the OS Rockets.
But it's the same concept, approach, strike, skirt edges, strike, repeat, and go home to reload.