Sorry, in all the other stuff we forgot about the proper terms. What you are actually talking about is the AIRCRAFT NEUTRAL POINT and not the Center of Gravity. The aircraft neutral point LOCATION is based on the balance point, wing area, tail moment arm length and the stabilizer area and relates to a term called Tail Volume Coefficient. An imaginary ( as in "with no dimensional units") value that describes how we can expect the model to handle based on these factors. To fly in a stable manner the CG must be on or slightly ahead of this neutral point. Otherwise it's like trying to fly an arrow backwards.

Models HAVE flown as free flight contest types with the neutral points and balance points back around the location of your pivot but they have odd looking EXTREMELY long fuselages and very large tail areas. I wasn't kidding when I suggested that you can only fly with the CG back at that location IF you tripled the tail boom lengths and doubled the tail area. Of course such a move would bring it's OWN balancing challenges.

Changing to a lifting tail with the present configuration WON'T DO A DARN THING. It's all about surface areas and moment arm lengths. The airfoil is just selected based on the other stuff to help it do the job that the other stuff has placed onto it.

This was also why I was suggesting that since you're so close to finishing it just use the present model as a hovering test mule that can tilt the engine forward and back a small amount to test your theories. With the layout as it is and the balance point back where it will be with the engine in it's present location you will not be able to fly in a normal manner. It'll be like trying to fly an arrow backwards. From what I can see in the pic I estimate the balance point for normal flight would require that the model balance at the prop nut with the engine down. I suspect you're a LONG way from that. And, of course, it needs to balance on the pivot with the engine in the hover mode.

I know this isn't happy news to you but you've sort of painted yourself into a corner. There's no "magic pill" that can alter the physics of the situation at this point. Cut your losses and complete the current model as a hover test mule. The next one will be twice as good.

PS: You "MAY" be able to get away with the CG back there but it would require changing over to a tandem wing arrangment. If the stabilizer was replaced by ANOTHER WING of the same size as your current one then the neutral point WOULD move back to about the position you require. Increasing the stabilizer up to the size of a wing being what is required to move the neutral point back to a position slightly behind the pivot. But then that would greatly increase the problems of moving the balance point back forward so you're right back where you started from but at least with a tandem arrangement you can then add a long nose boom so the amount of nose weight is decreased. As long as the overall weight does not go up so high that the model weighs more than the thrust you have available.