for what it’s worth i have a different solution to the problem of the OP’s strap breaking on the tattico mount. I have a tattico and love the thing, about 2/3 as good as my floor pump which is saying something for a pump that small. Last year I got a bike that has some aero touches like the down tube and though i bought an extra tattico holder for the new bike i thought it counterproductive to mess up the lines by putting the mount on there. So i put the pump in my center back pocket and had no problems, even when i took a spill on a forest road descent on a gravel ride it didn’t pop out though it always worried me. So this year after seeing in some silca advert, I bought their mattone underseat bag with the boa strap and did like they did where i use that boa strap to secure the tattico behind and underneath the saddle. Works great and though i check and make sure it’s still there constantly because i’m paranoid i haven’t had any reason to be so.
which brings to mind speaking of silca one last time, for those sick of rubber bands and velcro you could buy their mattone or mondrian gear keg with the boa strap and use that separately to secure what have you.