I really thought the four kinds of charge and the four forces needed unifying. How silly of me!
Nature does not recognize multiple kinds of forces. Nature recognizes one kind of force; the kind that produces acceleration. (Actually Nature just recognizes acceleration, and their equal-but-opposite counterparts, scaled by relative mass.)
In other words, we could have predicted a priori that the forces would unify under some condition, which turns out to be high energies.
While yes there are certainly sub-types of force which interact differently with the various charges, ultimately it could be described with just a list of particles and the forces between them, without reference to charge or the 'kind' of force at all. There are not four forces. There is one force.
Having realized this, I discovered the thing I want to share with you, dear reader. There's a very good reason that Quantum Mechanics and General Relativity, and it is not just the problem of what time is. The above analysis is not complete.
The accelerations described by GR are, in fact, not accelerations at all. To the best of our knowledge, when you are in free fall, you aren't actually falling. You're moving in a straight line, according to your relative spatial geometry. Instead the Earth is accelerating up to meet you, under the continual force applied by the deeper layers.
In other words, you're going straight when you're falling, and you're accelerating when you're standing still. The reason for this is a simple recognition; neglecting gravity, when you're falling your forces are balanced. When you're standing still, you have to have an upward force constantly or you would continue going downward.
This upward force continually curves your straight line, technically called a geodesic.
The reason you can transform gravity to be a deformation of space and not the other forces is simply because everything has the gravity-type charge, mass, but not everything has electric charge or colour charge. This also solves the problem of why momentum uses the gravity charge, not the electric charge or colour charge, or its own charge; electric forces must push against mass, but gravity just bends straight lines. (A full explanation is unfortunately very long.) This is also why mass cancels out during acceleration calculations for gravity.
This is why photons bend noticeably around heavy things. They're going in a straight line, relative to them, but the space they're going through is bent. Photons have no mass; applying forces to them doesn't make any sense; F=ma=0a=0. All forces on photons are zero. (This is complicated by relativistic mass and E=mc2.)
To sum that, it isn't that there's not four forces, but rather one. There aren't three, but rather one. The forces of Quantum Field Theory are all forces which cause accelerations. GR describes the bending of the background upon which QFT operates. Gravity doesn't have a charge and thus probably is not the result of some symmetry. It's just...different.
But yes, figuring out what time is would help a lot too.