I found that BH-55 matches series 2 quite well and that guys from RRS use it this way as well.
It doesn't seem any wider than the base of platform, a bit wider that the elevated part though.
Yes, it was the elevated part that I was referring to as the platform, and you can see the overhang compared to the BH-55 on a 3-series (pics below).
Actually, the leveling base platform is larger than the 2-series base platform - the diamater of the leveling base for the 2-series is the same as the 3-series platforms, and perfectly matched to the BH-55 base with no overhang. That's by design, because the larger base of pano gear (PCL-1, PG-02 horizontal base, which are the same base diameter as the BH-55) would block part of the bubble level on the leveling base.
The leveling base also adds a couple inches to the height.
If your only use for the leveling base is for panos, another option would be the PCL-1 panning clamp w/ dovetail. With the leveling base and a ballhead, you must level twice - the base for the panning, but you also need to level the ballhead clamp so the series of shots is level. The PCL-1 w/ dovetail clamps into the ballhead, so you just have to level the ballhead clamp and you're done. That option also gives more tilt freedom that the leveling base, which is limited to 15°. Of course, that option is $76 more than the series-2 leveling base - again, paying for convenience.
I noticed you asked about the height of the TVC-24L with 3 sections extended, that's 50" - a little shorter than the 52.4" height of the -23. That info is actually on the RRS specs page for the TVC-24L.