Comparing the Felt to the LOOK 566, you will quickly see that a medium 566 is a larger size with a much taller head tube (44mm). The reach is actually about the same once the STA is taken into account. The 52cm Felt is really comparable to a 51cm LOOK.

If the LOOK had a 30mm stack of spacers and perhaps a 96 degree stem, the bars might have been 40-60mm higher than your Felt.

If you post your current setup, I could propose some options. If your stem is already flipped up, then I'd need to know the angle or at least the brand, since most brands only offer a couple of angles.

The steepest road bike stem is usually a 73 (-17) flipped up to 107 (+17). That angle will raise the bars about 60mm more than the lowest (73) degree angle. The horizontal length of the stem will be two sizes shorter than the advertised length, so a 110mm stem is needed just to get a 90mm horizontal length.