Im not familiar with Tiny Tush but I am familiar with that barn animal smell. LOL I have found that the synthetic materials can stink A LOT worse than natural fibers. All of my dipes are natural fiber but I have some soakers that are made from micro fiber and boy can they get bad. I have 3 boys that I cloth diapered but currently I only have one that is still in dipes.
So I 'd put my money on the synthetic stink rather than the need to strip dipers that you just recentely bought although as a previous poster mentioned, diaper rash cream can really gunk up the diapers and make them absorbant .
I have an HE washer too and this is my routien.
Now, wet diapers in a WB for two whole days can get a little hairy believe me! I came up with this process when I was newly pregnant. I HAD to to find something to get rid of the smell as much as I possibly could
I use a "rice paper" liner to make the removal of the big stuff easy and I rinse the diaper with water, squeeze out and leave out to air dry. It doesnt really take up that much space I use a clothes drying rack right now but I have in the past used a towel hanging rack in the bathroom.
This might not be an option for you, as you said you live in an apartment and have 2 in diapers. But it is sooo well worth it to let them dry out in between washes, you just have to find a creative space to hang them, like in the bathroom or laundry room, a friend or mine hung them on her covered patio.
When they are dry or dry enough, I store them in my wet bag.
On my third night I load the the washer and set to quick wash, for the initial rinse. My second wash is my sanitize cycle, I use homemade detergent so I don't have a favorite brand at the moment. My third wash is on the delicate cycle, it will give you the highest water level. I just use water for this cycle, no soap. Also once a month I put OxyClean into my sanitize cycle and vinegar into my rinse cycle.
Works like a charm!
I wish I could help you with the size thing. I make my own diapers so I just make them as needed. Have you looked into anything like Diaper Swappers? It's a big online community that would certainly have the information you need.
http://www.diaperswappers.com/
Good luck!!