Re: the router, what are the odds that this behavior would occur on two different routers and networks? I doubt the routers are the culprit since no other Wifi enabled devices dropout like this.
It's not necessarily the router that's the 'culprit', but rather the combination of the router and the Wi-Fi. Wi-Fi interoperability is a finicky thing (back in the days when laptops were first getting Wi-Fi, Intel poured a tonne of money into its "Centrino" brand which included interoperability testing, because the combination of somedevices often failed to work properly, even though most did.)
That's why knowing the router is important for Microsoft to troubleshoot the problem, because without having the problematic router, it might not be able to reproduce the problem you're having with the Wi-Fi on the Surface.