How do I choose the correct airfoil?
Terms fist, to avoid any misunderstandings:

What you call cuboids is normally called a wing spar. It consists of spar caps for the tension and compression loads and a web between the caps to transmit shear. And yes, it runs all the way from one wingtip to the other.

The spar carries the bending moment which has its maximum at the center and is zero at the tips (unless you use winglets). The more distance there is between the two spar caps, the lighter the spar can be built, so a thick mid-wing airfoil helps. Your choice of the NACA 64₃618 is a good start. I would advise, however, to taper the wing to something like a NACA 63₃412 at the tip. Thinner airfoils have lower minimum drag and higher maximum lift coefficients which helps to avoid the tip stalling first.

Or you move to newer airfoils which have been optimised for longer laminar boundary layer runs. Since you plan to use carbon/epoxy for the wings, you might take advantage of the exceptionally smooth surface this makes possible. The NASA contribution is of course the NLF series, NLF standing for natural laminar flow. The NLF(1)-0416 or the NLF(1)-0215 would be possible candidates. Even better designs might be possible when you search for modern glider airfoils; however, the published ones generally are at least 30 years old. Glider airfoils are optimised for minimum Reynolds numbers of around 1 million; when used in a GA aircraft this might be a bit conservative but could fit well to your low speed requirements.

The ultimate step could be to design your own airfoil. Take my glider recommendation and use XFOIL to tweak it to what you really need.

One last word on your choice of flaps:

When the inboard span uses powerful slotted flaps, their increased circulation will change airflow at the outer wing in such a way that the outer wing will stall before the inner wing had a chance to demonstrate it's lift potential. Either stay with plain flaps (for which the HQ-17 was designed - make sure you calculate it with a positive flap deflection at slow and negative at fast flight speed!) or add slats to the outer wing. In order to keep complexity manageable, I would recommend to use plain flaps and flaperons over the full span.