You're thinner section will be fine. Many models work with a 10 to 11% airfoil without issue and the shape you're using will scale decently enough to fit. I guess I was thinking that you were going to thin it to well under 10% and that can have problems.

In any event you need to ensure that the spars are well bonded to the phenolic tubing. I'd make it just a hair larger in thickness, maybe a 1/6 or so, and then pack the resulting 1/32 inch gaps above and below with a mix of epoxy and microballons made thick enough to form a nice putty. You'll need to use saran wrap and some foam rubber to "clamp" the putty in place until cures or it'll run out leaving voids.

Making the wing thinner will also put more load on the spars. I would suggest you take a page from the glider folks and use 1/8 x 1/2 spruce top and bottom caps and then box them front and back between the ribs with 3/32 HARD balsa with the grain running vertical on the webs.

But frankly I don't see what the big deal is. Use the larger thickness, punch the holes for the tubes so they are contacting one spar and then fill in the gap. The wing will have a more gentle stall with the thicker section, won't tend to speed up so quickly when the nose drops and will be stronger thanks to the deeper spar design. As a bonus the 1/4 deep part of the ribs will hold them together while you build in the tubes. In any event you should stick with the webbing of the top and bottom caps. You still need to bond the tube to the spar caps. That's a must do regardless of how you do the final job.