> galaxies further away are moving faster than that
No, you have it backwards. Accelerating expansion means, roughly speaking, that we see galaxies further away moving away slower than a "uniform" expansion would predict. Remember that we are seeing galaxies further away as they were a longer period of time ago--so "accelerating expansion" means the universe was expanding slower then, when the light was emitted, than it is now.
Actually, though, we don't observe the distance to a galaxy directly. We infer it from other observations. The actual observed quantities are redshift, brightness, and angular size, and the relationship between those three observed quantities is what tells us the expansion history of the universe.
No, you have it backwards. Accelerating expansion means, roughly speaking, that we see galaxies further away moving away slower than a "uniform" expansion would predict. Remember that we are seeing galaxies further away as they were a longer period of time ago--so "accelerating expansion" means the universe was expanding slower then, when the light was emitted, than it is now.
Actually, though, we don't observe the distance to a galaxy directly. We infer it from other observations. The actual observed quantities are redshift, brightness, and angular size, and the relationship between those three observed quantities is what tells us the expansion history of the universe.