I've chased the last two seasons exclusively with a 128GB flavor of the original Surface Pro and I love it.
I have it held in a RAM mount with the X-Grip III and it's very sturdy and robust. I use the TomTom GPS MkII which is a bluetooth GPS. I keep this underneath my armrest plugged into the accessory power there and it has no problem obtaining signal. I opted for bluetooth GPS over the BU-353 puck because the Surface only has a single USB port and I'd rather keep that open for other things like downloading photos/video. I know Globalsat (the BU-353 guys) also have bluetooth receivers, but I haven't tried one.
For mapping I use the Microsoft Maps app. I can't remember if it's a default program or if you have to grab it from the Windows Store, but either way I prefer it over other mapping software because it's very touch friendly. It requires connectivity to use it, of course, so I have Streets and Trips on the desktop to fall back on if I lose signal.
There is a caveat to using GPS devices with Windows Apps (read: non-desktop applications) in that it uses Windows Location Services. This does not normally interact with serial devices. The Surface tablets do not have a GPS receiver built in, this is a bummer. To get around this problem you will need a NMEA/COM to Location Services middleman software which you can find here:
http://www.turboirc.com/gps7/ I actually need to look at that myself since it's been updated, but the GPS Direct application is what you'll need. This will allow your Windows Store Apps to use your COM port GPS either directly or via GPS Gate. I have a whole writeup on this I did on my blog a couple years ago here:
http://www.nicknoltewx.com/blog/2013/03/15/gps-devices-in-windows-8-apps/ How I have it setup is GPSGate grabs the Bluetooth signal splits it out to 4 virtual COM ports, one of which I use as the input to the GPS Direct (GPS Sensor 7 software), then that forwards it to Windows Location Service automatically which allows for GPS stream use in apps. Desktop software like GR or Streets and Trips use one of the Virtual COM ports like usual.
GRLevel3 is definitely usable with the touchscreen. It takes some getting used to if you need to tap some of the toolbar icons, but it's not a problem for me. Pinch to zoom and swipe to pan works as expected, double tapping on a radar site switches and things like that. But, as you describe, you may have trouble tapping play/pause in GR if you're driving down a washboard road.
I don't find the poor organization or lack of apps in the Windows Store to be a big problem. There are solutions to most problems, otherwise you can always use the desktop. I can understand how this might be a dealbreaker for some, but it's a non-issue for me.
As far as computing power goes, I have no problems downloading video to the Surface, tossing it into Sony Movie Studio Platinum, doing some edits, rendering and uploading via FTP. Lightroom works great on the surface, although the screen space is a little cramped since it has all kinds of panels everywhere, but you can adjust that to work best for you. The power is there, it's not a problem.
I'm happy to see more and more people picking up tablets for chasing. I think it is an obvious solution as it eliminates some cabin clutter as well as a physical keyboard in favor of a more compact and lightweight footprint with a very high quality touchscreen. I think people who have talked to me know I'm pretty much a Surface Pro fanboy, but it gets the job done for my needs better than anything else I've used, and I've chased with a Dell Mini 9, a regular Toshiba Laptop and an iPad over the last 5 years. But, each person has their own needs and preferences. I'm thinking about upgrading to a Pro 3 for this season, but I haven't pulled the trigger yet