ahh, this is gonna be a bit tough to model. i can only give ideas to try, but not much more help than that. hopefully someone else can help you refine one…
- lofting curves… for this you’d have the edge curves, right before the top part starts its bevel, and a centerline curve at a higher elevation. then you’d loft over them to create your curved front face to give the final result. this probably would have to be done in sections, but fortunatly there’s a lot of repetition, so a section and rotate it.
- cloth inflation, this one i’ve not done but once… but you could mark that top flat face as a “cloth” and inflate it from behind. there are some plugins for this, but this is pretty complex geometry, so not sure how it’d fare…
hope there’s some help you can glean from these.