I am at a loss to even venture a guess, I'm not even sure if I can assure our concerned daughter that it doesn't bite. We have found 3 or 4 over the past few weeks, usually alone and somewhat docile but moving. Usually crawling slowly across the floor, the last guy attempted to fly but could not quite leave the ground (see action shot below).
Length estimated at 15 mm. Using only a 5-year-old point-and-shoot camera (I guess that's old in electronic years), I must say I'm surprised some of them sort of turned out.
UPDATE: This bug has been identified as a Wood Wasp (a type of Sawfly) by 'The Home Bug Gardener' and species confirmed by Robin Leech via Albertabugs via Henri Goulet: "This is a Xiphydriidae. The species is Xiphydria mellipes associated only with small (less than 3 inch) branches of dead birch." Thanks to everyone for their help!
The bug's home is clearly small diameter paper birch branches we cut last year and placed inside for use as coat/hat racks. The wood wasps are waking up confused and disoriented in their new interior habitat! I have confirmed online that wood wasps do not sting and do not pose a threat to structural wood in the house (I guess that assumes small diameter birch is not used for home construction in this case!).
I think this helps with our decision to keep at least some of our dying paper birch as a bug and bird sanctuary (I was debating chopping them down). I wonder who else is living in there??