I'll assume it's a 30 amp service.
Camping World sells a correct port that can be installed in the side of your camper, and replaces that little hatch that your cord goes through. It gives you a twist-lock style receptacle for better connection security. I have the pieces to do the mod, and it basically consists of pulling almost all of your cord out, cutting it off about 8 inches outside the wall, and wire, attach and seal the new receptacle into the outside wall. You then have to attach and wire the correct twist-lock cord end on the cutoff end of your original cord. Becomes a "drop" cord for your camper. You might have to scare up an electrical supply house for the right cord end. My local home improvement outlets didn't carry it, so that's what I ended up doing. Cost a pretty penny for the cord end, but I wanted that, and it's better quality than they would have had anyway.
I agree with your assesment of the little compartment to stuff your 25 foot, 10/3 SOW cord into, through a 7/8" hole in the side of your RV. P-I-T-A, in big, 2-foot tall capital letters. (And the bends and twists aren't good for the cord, either.)
Roger