Actually, I have done exactly what you're talking about.  Let's say you want a 2cm strip of velcro.  Cut a piece that is about 6 cm.  Tape this or glue it to your PM piece as you normally would.  Then sew the whole thing using sturdy thread...if you can't access the underside of the PM then you obviously couldn't do this step.  If that is the case use glue instead of relying on the velcro's adhesive.  Then you can cover the outer 2cm edges with paper mache leaving the middle 2cm exposed.  This way the velcro strip sort of becomes part of the paper mache rather than simply being stuck onto it.

I don't think that pulping around it will help at all.  You haven't said what strength of pull is applied but a lot depends on that.  Firstly, the paper layers to which you apply the Velcro must be strong enough to withstand the strongest pull that will be applied.  You may need to incorporate some fabric in the laminate, with strong PVA, extending it a couple of inches beyond where the Velcro will be fixed.
The idea of incorporating the Velcro within the layers is good and I would use staples, flattening them with a hammer before layering over them.
If one of these ideas doesn't work, give us a more detailed description of what you are making.

DavidO

Thanks for your input!!  I think the layers underneath will be strong enough - it is actually gauze plaster cloth that I layered over the paper mache on the hat brim area because I was afraid the paper by itself would tear away from the velcro/glue combo. It has held fine so far and I work the velcro repeatedly.

What I make are Santa wall hangings and I make the hat and the fur brim removeable so people can change colors and styles. I make a lot of them and use five different tabs of velcro to secure the brim. I want to keep my price down, so I need to find a solution that is not too time consuming labor-wise.  It really is only two of the tabs that keep coming loose, on the side of the brim that you grasp to pull off. Today I replaced the two tabs with one 4 x 4 inch piece of velcro that I rounded the corners of. So far, so good - it seems to spread the pulling force over a larger area.  I will use this "fix" on the Santas I currently have done but I think I'll experiment with your suggestions on the next set that I work up.

Hope this makes sense, hard to describe without pictures. Thank you all again for your advice, I really appreciate it!