i rarely get the flaps outside hueco too. krazy glue is good for securing tape as well, usually on the backside of the finger so when i peel it off it doesn't make the split/cut/flap any worse. Makes it so you can use less tape and feel less like you are clubbing baby seals.
I've been using the krazy glue dispenser that looks like a nail polish brush, awesome for application, but the top always gets glued to the jar or it ends up cracking at the top. disaster waiting to happen in a backpack.
I have the plastic case you showed in my glove compartment. Found it in an HEB by PMFB, where I get the worst flappers ever. I also keep some sandpaper in there (a trick a fellow b.commer showed me to prevent flappers from happening in the first place), nail clippers, and tape. I rarely get flappers anymore, but the kit is there in case.
bleeding through the tape...now dabbed with chalk....does this provide an unsporting amount of friction? bloody boulder problems rule cause its like having multicolored tick marks