is there a better bandage than this in a pinch ?

been there done that.

I always keep some horse bandage around in the shop, house, barn, tractors and vehicles. The other one is to keep a tampon as well as it absorbes bloods from major cuts. Horse bandages can usually be found at TSC or vet places.

http://www.drsfostersmith.com/product/prod_display.cfm?pcatid=16434

It only sticks to itself and you can cram paper towels underneath and wrap it up.
I had a splint on my one hand due to a pinky finger fracture, and it was wrapped with medical tape.
I still had to milk cows despite dr orders. So the horse bandage came in handy and i wrapped it up with blue or red depending on the mood. Milked cows and got the bandage dirty. Simply removed bandage afterwards and the medical wrap was still clean.

Yes, injuries/sickness cannot keep a family dairy farmer from milking cows because it has to be done. Whens the last time you had a union worker not milk the system?