V much doubt you will get it reg as a camper, rules have changed, private hgv most likely.
France would save you on peage if sub 3m height, more places to park at night too if sub 3. 3m
Mont blanc tunnel etc v much cheaper to be a class 2 at sub 3m
Italy on axles so no biggie, German is currently over 7.5t for tolls at present (might go 3.5t at some point) so no probs either, Austria & Switzerland & Czech are over 3.5t for larger tolls & a toll box is just a cheap vignette under, toll box for Belgium over 3.5t too, no vignette for under.
Cant help with Portugal, Spain I can’t remember.
Is a site with all the euro info needed info for hgv, can’t remember it now quick Google should find it