> You can always measure when you are in a gravitational field (or being accelerated). For that reason, it wouldn't be correct to say you don't feel any force from gravity.

When astronauts do low-G training in the vomit comet they are definitely in a gravitational field and (in your words) are "being accelerated". But they feel no force of gravity.

Or as a similar thought experiment: imagine that I am in a spaceship with no windows traveling at a constant speed far from any large mass. If the spaceship started to approach a large planet, would I feel a force of gravity pulling me in toward the planet stronger and stronger as I approached it? My understanding of relativity is no: since I am in an inertial reference frame it makes no difference to me.

> Also with gravity we feel the force of gravity pushing us downward

Isn’t it the other way around in relativity? When you are in free fall, you feel no force from gravity. When you are standing still you feel the force of the ground accelerating upwards into you.