Bad, Flush Doggy, Bad!

The disappointment is almost too much to bear. Ok, it's not that bad. But it's close. I was so excited and I've been let down, hard.  I had ordered these flushable dog poop bags on Amazon and I was anticipating the joy of watching those white bags swirl down the porcelain bowl and away from my life.  I could picture the clean beauty that would be my outdoor garbage can, stink free and easy. They're called Flush Doggy and they purport to be "100% Flushable & Biodegradable Poop Bags." In my personal experience, this is a bold-faced lie.
After researching a few options and watching some very strange testimonials on YouTube, I choose Flush Doggy because they seemed to be the right product for the job.

The instructions on how to use the bag is quite clear.
1. pick up poop
2. flush it

Well step 1 was easy enough. It was step 2 I had a problem with. It's always #2 that causes a problem, isn't it? 
Now, I'm not naive, I knew there was a good chance that this whole thing could backfire (haha) and therefore, I was prepared.  Toilet lid, up! Rain boots, on! Towels and plunger, at hand!  Cautiously, I placed the poo bag in the water.  My expectation was that the bag would instantly start to dissolve, based on videos that I'd watched.  This did not happen. Nothing happened. The bag sat there looking baggish.  The only change was that it really started to smell like dog shit in my tiny, unventilated bathroom. So, I flushed.
Instantly, the bag disappeared and my toilet started to fill to the brim with water.  Dammit! I waited, though, and watched. The water level stopped rising and just leveled off. Some water was still trickling in but it was also going down the same amount. After deciding to walk away and ignore the whole situation for a few minutes, I turned my back on the toilet. A gurgling, sucking, shlurping sound made me spin back around in time to witness the water suddenly vanish down into the pipes. The commode refilled in it's normal manner. I was relieved (haha).  
Two days later, I decided to give it another go (enough with the potty humor, already!). What had I done wrong the first time? Did I not wait long enough before flushing? This time, I would close the lid and go into the other room and give it some rest in the water for a bit. Surely, this was the answer.
This was not the answer.
I had to plunge and Sam witnessed it. No more Flush Doggy for this family. I'm returning them and getting my money back. 
So, back to the drawing board on this issue.  Maybe a different brand works better? Before I try another flushable bag, I'm going to have to find a different toilet to use, because those things are not going in mine!  
I had a discussion last night with some friends on the subject and they brought up some good ideas.  Perhaps some sort of diaper pail/cloth diaper type system will work. I'm looking into it.