Concur. Cmaj is a chord you really can't ignore in the repetoire, and a 3rd fret barre Cmaj whilst it still sounds pretty, fuller on electric or e-acoustic than pure acoustic, still doesn't have that open chord timbre. It could also be a progression change PITA unless using other barres in the progression.

All that said you may have to compromise with it or resort to or a "lazy C" if you can't figure out a way to finger conventional open Cmaj. If it were me, I'd take a step back, analyse the why and correct it by trial and error accompanied by hours of perseverence and repetition, repetition, more repetion if necessary. As iterated in my earlier post, open C is pretty easy on the APX600/F310 necks even for the smaller hand and fingers, assuming no injuries, osteo or other physically inhibiting factors.

Although it shouldn't be a factor, I have to say I detest Dreadnoughts. Could the way you are holding/resting the body and resultant neck/fretting hand 'body English' in any way be interfering with your hand placement and fretting of C? Perhaps pop into a store and try something like the APX. Make sure it's a 600 not the 500III it succeeded, as the 500 & 700, 800 all have wider string spacing and the latter series wider nuts if I recall accurately.

Inexpensive alternatives with pretty tone are Cort's AF510 and cutaway AF515CE. Both are smaller Concert bodies, slimmer depth athough not slimline, and whilst the necks are more conventional and string spacing wider, they are both a delight to fret with no issues achieving any of the stretchier open chords like Fmaj.The AF510 comes in inexpensive pure acoustic or electric acoustic versions (CE suffix), the 515 is CE only and thus dearer. I've many hours hands on the AF510s. Here is what one sounds like by a better player than the orator in the previous descriptive link. Impressive guitar for so little money. They perform way above their price point, and importantly, are a pleasure to fret.

GL with Cmaj. You will find a way.