matimeo, could you clarify your goals? So far it seems to me you really want to do is change to road handlebars & brifters, which is quite understandable. I agree keeping the 7spd freewheel configuration with the existing wheelset is one option you should keep in mind. 7-speed freewheels are still readily available and affordable new, so this is by no means a dead end. You do want to stay away from 8spd (or higher) freewheels, as you are correct; reports are that the length of the axle required makes it prone to bending or breaking.
I've read that there are ways to set up an 8-speed indexed shifter to shift 7 speeds; so if you're interested in that option, do some searching. That would open up the option of a 3x8 brifter setup which should be readily available.
Depending on which front shifter you go with , you may have to change the front derailler to one that's compatible with the shifter.