The force is real, curvature doesn´t make a difference. Saying that it is caused by curvature is wrong, because the curving has to be done by a force that is equal in power.
Unifying? Well, heat is electromagnetic radiation in units W/m^2, and gravity is a force in units Nm. To compare the force and the heat like in a heat engine with the first law, set gravity to act as stress/pressure/thermal resistance, in units Nm^2. Then heat emission at earth surface is equal to the source power density of a gravitational force as resistance, $4g^2$.
Surface temperature at 287K is equal to heat flow of 383W/m^2, and a thermal resistance of $383Nm^2=4g^2$.
First law of thermodynamics with irradiation by the sun(TSI, $1360.8W/m^2$) as dU:
$TSI(dU)-4g^2(W)=4Q=4*244.5W/m^2=$ effective emission at 256K
So, gravity and heat emission from effective temperature, as heat and work in the first law. That is unified enough for me.
I saw something about charge in another answer. It is interesting that solar heating and gravity is equal in the equation for the electric field inside a hollow sphere with a ball at the center, $TSI/(4/3)=4/3*8g^2$
The relation where volume holds the sum of sources for the surface flux imitates real relationships accurately. This is Gauss law for gravity and the shell theorem. It fits perfectly on earth, and the idea of charges, potentials, in the heat flow, makes me think electricity seems to hold the answers to gravity and hot bodies in space.