I re-read your post and I can't imagine the "drop in" RV black tank pouch things building up and clogging your outlet. They are designed to dissolve and do so pretty well.
Here's something you can do though. Add some water to your toilet and then drop the pouch in the toilet. Let it sit. They take about 2 minutes and the outer plastic is dissolved. You can see it this way. Then let the contents of the toilet "go". But you'll see what I mean.
An another note, I feel you are wasting your money on using those black tank pouches and liquids. There are other and better and cheaper ways to accomplish the same thing, that have an end result even better.
It's call the "Geo Method". Look it up on the internet. But basically, it's a method for keeping the tanks clean and no odor forming by using simple household products instead of chemical designated for "RV use"... which are usually very expensive, when you really think about it.
What is the "Geo Method"? Simply put, you use dishwashing liquid, or laundry detergent, or bleach, or water softener for laundry like Calgon, down the toilet. These products keep the insides of the tanks slippery, preventing less build up over time, cost less, are environmental and septic tank friendly, and are readily available products that can be purchased anywhere.
Very simply, when leaving the campground, dump your tanks. Then add a few gallons of water, drop in some laundry detergent, softener, and/or bleach (like what you'd use in cloths washing machine) and drive to your next destination. The sloshing of the water while driving will pulverize the inside of your tanks, cleaning anything stuck to the sides, wash it out. Reach your destination, dump it and you'll be shocked what comes out.
Add some dishwashing liquid to the black tank. Use the toilet normal, and the dishwashing liquid will constantly help break down and attempt to clean anything that gets in there.
Of course, the cleaner the tank, the less smells you have too.
Hope this helps.