Vsync seems to limit framerates (in ME3)

This sounds like a result of freesync; if your framerate dips below the vsync refresh limit of 60, it'll dynamically stabilize to a lower refresh rate allowed by your monitor. I also have a freesync monitor fwiw (but with an Nvidia card; freesync still compatible).

One thing you can try; disable in-game vsync and use the in-game frame rate limit option (try 60). In your AMD control panel, enable both vsync and freesync. With Nvidia and gsync/freesync, you're supposed to disable in-game vsync while leaving control panel-level vsync enabled along with freesync, and I'm pretty sure it works the same way with AMD (almost everyone agrees on this).

If you still get no higher than 48 fps, try this: Disable the in-game frame limit (leave in-game vsync disabled) and instead use the frame limiter in the AMD control panel (I believe it's called Frame Rate Target Control). Set this to 3 below your monitor's refresh rate (if your monitor's refresh rate was 60, you'd set it to 57). This will ensure you don't get vsync-associated input lag and that freesync is active at all times.

The ideal solution would be the game's frame limiter, but sadly it doesn't have any options between 30 and 60.

Again, just to be clear, freesync itself limits frames (in a stepwise fashion depending on your performance in a given game), so seeing an apparent framerate cap below your refresh rate isn't necessarily abnormal behavior.