Purse abusers unite! Yes, mine is also a backpack-type purse. Have you had to wear it in front when visiting a museum? Uncomfortable & annoying! I can sling the straps through the top hook on mine, thus making the straps loop together to sling over my forearm, which I prefer rather than try to wear it frontwise.
Regarding travel soap with scraps, I don't like using scraps to wash my hands, they are just too small. And if you've just pumped gasoline or picked something up from the mud on your way to the public restroom, scraps just don't hold up well to vigorous enough friction (they fall into the sink before I can build up any lather).
I wish there were a way to dry out felted soap for travel purposes, but that's not really viable. I have a felted soap in my bathroom that has slivers & scraps inside and it produces fabulous suds and lather, but I know it would never dry out in my purse. It barely dries out on the sink saver, especially if I used it more than once or twice a day.
For several years,
@Susie has been making a
Soap2Go that is LS paste in a push-up or roll-up tube. I see many others have started making them as well and they are on sale in several Etsy stores now. It stands up well in a purse, but to be on the safe side, I still used a plastic ziplock baggie when I carried mine.