Bottom bracket sizing
Old-fashioned cup and cone type bottom brackets have one adjustable cup, with a lockring. The adjustable cup lets you set the bearing tightness, too loose and there is play, too tight and the spindle won’t turn.  

With a cartridge B.B., the bearings are self-contained and the cups are installed to a given torque which is normally pretty high as bike parts go. When the two sides are tightly installed, the spindle will turn freely. There is no finessing or adjustment of either cup required.

The problem of the spindle getting hard to turn when you tighten the cup, therefore, is not normal and indicates a problem. Hopefully it means the B.B. is worn out and replacing with a new one will solve it. I would try this first and see what happens. 

As for B.B. sizing, 68mm is the width of the shell, you can only use a 68mm B.B. 

The length of 118 mm is the spindle length. It determines the position of the cranks, outboard from the centre, and therefore, chainline. Make sure you understand this term. If 118mm gives the bike the correct chainline, then 118mm is the correct size and you should replace with the same size. Spindle length (118mm) is independent of (any) cup adjustment. 

Trying to avoid commenting on a given product, you might ask yourself if the only game in town arrived in that position by being crap... probably not. 

Update:
As you have a belt drive, achieving the correct position of the belt is critical, so you must use the correct size spindle, ie 118mm. The eccentric bottom bracket just allows you to adjust the belt tension, the B.B. dimensions are fixed.