I’ve found a workaround which works pretty well, partly alread described in this comment.
You need to download and install TypeLight (free for personal use), and open the Consolas.ttf file inside. To adjust the line spacing, go to Font -> Metrics -> Advanced and change the “Line Gap” to your desire (I changed “Type Line Gap” as well, but I have no idea what this actually does). I experimented a bit with a values and found around 730 to be similar to the 12 pixels spacing in IDEA.
To distinguish the modified font from the regular Consolas, I suggest changing the name of the font under Font -> Names (to “Consolas Spaced” or something). Save the font, double-click the file and choose “Install” from the preview dialog. Then (re)start Visual Studio, choose your modified font and you’re done.