I’ve had mixed success in various hotels, but found a fairly fool-proof way - albeit not fully in keeping with the “this little box does it all” ethos. It was prompted by me having a free Boingo account with my credit card, and for a couple of weeks on a particular site that a group of us were working on the only access that I could get was via Boingo (no cellular coverage, the site owner wasn’t happy giving us access to their wifi as we’d then be inside their network, but their internet was provided by BT Internet, who by default set their routers to give give guest internet-only access to their subscribers or Boingo). The problem with Boingo is it seems to need you to use their app to connect, and I had mixed luck doing that on the laptop then doing the Mac clone stuff.
So, having just replaced my Android phone, I use the old one to do the outward-facing connection to the hotel or commercial wifi, using Boingo or just logging in to their captive portal. That phone is plugged into my Slate’s USB port, select USB tethering on the Android phone and I can then share the connection onwards with the slate, all protected by the VPN from the slate to my brume back at base.
It does mean carrying another phone and cable with me, but that fits into the pouch with the slate so no big deal. That phone is bare except for the web browser and Boingo app. It’s not as neat as doing config changes on the slate, messing with DNS etc., but pretty much always just plugs in and works.