This can be solved using the radial menu.
-Michael
It is good that RadialMenu at least lets you remap squeeze'n'tap to emulate a middle-click, but it may be confusing or misleading (in a thread about how/why the barrel buttons don't work as expected) to call the issue "solved", when no, the barrel buttons still cannot be made to work as expected.
For the benefit of other readers, I'd like this to remain clear: RadialMenu does not enable a normal right-click or middle-click. The barrel buttons are only 'modifier' buttons like the awful 'Fn' key, and with no fix for this on the horizon, many programs that expect a three-button pointing device (or even a two-button pointer) will not be usable with the pen on the SP3, and you'd be better off with a Wacom, or a Wacom clone, or even using a mouse like a peasant.
Besides, if anyone from Microsoft is actually paying attention, we don't want them to go away thinking that the problem somehow resolved itself before they even had to schedule a meeting to figure out "what are those buttons doing there anyway".