I don't thing weight would be any issue, you don't need a full stocked tool box hidden in there. You just need some of the common/oh-shit stuff,,, Torx's, 6, 7, 8, 10, 12mm's, pliers, zipties, AAA card and that's about it. Anything else isn't a side of the road type repair situation, hence the AAA card.
I can see all that fitting in the divit on the top of the cover rather easily and discreetly.
Get some of that foam stuff, cut the tool shapes in, glue it in place on the cover, make a lid (ABS or 1/8" Plexiglass), use a piano hinge and screw through the cover (use fancy covers on the bottom side), drill through the cover for alignment pins on the front corners (ball and socket style, rubber grommet and plastic ball), make the 'lock' something simple like a snap.
Should all be able to fit near level and not look out of place one bit.
Thing you have to be wary of by mounting to the top is a panic stop or accident situation. You DO NOT want tools flying at you. So the lid must be secure and safe, no half-assing allowed. Guess that's the advantage of the under-mount style.
I really do like this idea and may just make one for myself ... just have to figure out where to get that foam stuff.