That acceleration is so subtle that only now we are accumulating evidence that it exists at all. And it will be decades, at least, until we have a good idea of the magnitude of this acceleration.
While there are many unknowns in current cosmology, there are no models without verified predictions, like the "FE models". And there are no objects accelerating at 9.8 m/s/s forever.
The entire visible universe (which is much larger than the visible FE universe) is accelerating away from itself at speeds you claim aren't known. Then you claim there are no objects accelerating at 9.8m/s^2 forever, when in fact every galaxy may in fact be accelerating well above that rate.
The redshift of many stars and galaxies has been measured for decades, and changes are insignificant or non measurable in that time frame. If there were any objects accelerating at anything close to 9.8 m/s^2 we would see it in the change of redshift or position in less than a day. Your argument is like saying that because you do not know how fast the San Andreas fault is moving, maybe it is moving at supersonic speeds and nobody has noticed.
The reasons for knowing that the whole universe is not accelerating at this rate, all in the same direction, is not this argument of energy just by itself, but anyone can see there is a lot of explaining to do if you say we are in a Saturn V kind of a rocket billions, trillions or maybe quadrillions of times the size of your known Earth.
It seems that a simpler explanation would be that they are all accelerating in one direction. Away from earth.
Since the OP is about the energy needed to accelerate Earth, then I guess we now have to ask where does the energy to accelerate them come from. And how they accelerate without any detectable output of energy.
IF the earth is accelerating at 9.81m/s^2
we could say that the speed of the earth is very close to the speed of light (1)
E=F*d (2)
F=m*a (3)
m=m(0)/(1-(v/c)^2)^(1/2) (4)
v=c (1)
=> m=infinite (4, m(0) exists and is more than zero)
=> F=infinite (3, a is acceleration = 9.81m/s^2)
=> E=infinite (2, d>0: earth is moving => in one second the earth has traveled a certain distance)
even for accelerating the earth only one second you'll need an infinite amount of energy (IF FET is correct, ....
NOT)