I thought downgrading was necessary as well to run LCPDFR. Everyone is saying 1.0.7.0 is the most stable. So I tried that. It's quite easy, and yes it does indeed remove the loading of the R* Launcher in the process by using the xlive.dll. So, after that, a fresh install of LCPD First Response (Legacy Edition) 1.1, and it just CTD's 10 seconds after loading into the game (when you are standing in your safehouse).
Note: I'm not interested in LCPDFR with MP ability, so I opted to use xlive.dll instead of dsound.dll during the downgrade process.)
Out of curiosity, I read the LCPD First Response (Legacy Edition) 1.1 download page again, and noticed that it says "LCPDFR 1.1 should be installed on a clean installation of the GTA IV: Complete Edition downloaded through the Rockstar Launcher." Which means NOT downgraded, I would assume. So it's at 1.2.0.59.
But because of this, the R* Launcher is not disabled. So I think the question is, how to disable the R* Launcher without downgrading?