I'm playing with the idea of picking up a rod to use for jigs and toads, as I want to learn and get better with  both those applications.  But based on the waters I fish, I can't really imagine going over 3/8 oz jigs much if at all.

With that said, is a H rod the best bet?  I was thinking about a BPS Pro Qualifier 7 MH that is recommeneded for I believe 3/8 to 1.5 oz lures.  Any advice on whether or not a MH would likely have enough backbone for pulling bass out of the slop?

I would go heavy for that.  JMHO

i pitch with an all star im10x big boys 6-10 inch rod.it's extra heavy and will pull anything out of the slop.

Take a look at the Shimano Crucial 7'6" MH trigger rod (Flipping stick).   I'm picking one up in a couple of weeks to us for Frogs, Jigs, Flippin and spinnerbaits.  Rod is surprising light for it's size.  Has a nice tip action and plenty of backbone to set hooks or pull fish out of slop.  Could also use it as a shinner rod.

Cheers

If you are really going to be casting 3/8 oz baits, a rod rated for baits 1/4-3/4 oz lures would probably suit you better.  That does however seem really light for jigs and toads. My frog rod is a MH power St. Croix rated for 3/8 to 1 oz baits. I also prefer 7'. Mine is a AC70MHF, I recommend you look at it.

I think Kistler makes the exact rod your looking for.  the Mg Jig and Toad special.  It's a 7' heavy power, fast action rod.  but its not just a broom stick, it will cast lures from 1/4 to 1 1/2 oz.  great rod and its not too big and bulky either.

If you are really going to be casting 3/8 oz baits, a rod rated for baits 1/4-3/4 oz lures would probably suit you better. That does however seem really light for jigs and toads. My frog rod is a MH power St. Croix rated for 3/8 to 1 oz baits. I also prefer 7'. Mine is a AC70MHF, I recommend you look at it.

I agree with with that. I have the same rod and love it for jigs and frogs. I can fell the fish just tap the jig. It also helps when I use braid.

I have a 6'10 Team Allstar that works well. I am about to buy the Daiwa Light and tough 7'4" frog rod, just to add another flipping stick to my arsenal.