Welcome to the forum. I shouldn't really be saying that though because I just joined too. Having fun so far!
You could try lapping 1/8" on scrap, but I think the router might just destabilize the other layers that you're trying to keep. 1/16" is pretty thin. You'd need some high quality ply! But you should try it.
I used lap joints for the 1/2" exterior wall, and no complaints. I did 1/8" on my inside, and I just did butt joints with a 6" x 1/8" backer of the same stuff. Plan to do the same for the roof. Of course, this means you'll need to cut out the 6" x 1/8" notch to make the ply lie flat. Not a problem with my 1" foam core ... maybe 30 min with the belt sander. If you're doing 3/4" core, why not leave enough 3/4" where the 1/8" joins is to hold the ply on? You could also do a fibreglass joint.
Either way, make sure it's either pretty or hidden. Mine's the inside layer, natural poly finish, and the butt joints were going to be a little ugly. So, I squirrelled them away in the galley to avoid having to fix them. I also found that the 1/8" (mine's straight sanded birch, the rest is Baltic) is very dry and chips a LOT, so maybe masking tape the cut line or sandwich with scrap to prevent that. Cutting with a router produces a nice edge though.
Check out my Budget and Sourcing page (below) ... I'm in Canada too (Salmon Arm, BC, in the Shuswap), and I've had to do some searching to find a couple things. Mind you, Saskatoon is a little bigger and a bit more industrial in nature, so you're probably finding what you need there. I find a lot of the parts discussed on this forum pretty well double in price by the time shipping, handling, brokerage, duty and tax are slapped on!