If it Fails
If the law you propose passes, great. I'm not sure we need it with regard to 16-11-127, because I'm not convinced that having a gun in your car as you drive into and park in the parking lot of a restaurant, a bowling alley, or a government building is "carrying a weapon to..." said places. Right now, there is room to argue that if the building itself is where people gather, only the building is off-limits not the parking lot.
Of course you can't say the same thing about airports or MARTA stations, because the law actually defines what those places are, and it includes the parking areas. That really needs to be changed, because it's clear the law is against us as written.
Now, if we try and lose, here's the down side. The fact that the legislature was given the opportunity to allow guns in parking lots of public gathering sites and CHOSE NOT TO AMEND THE LAW would be evidence (powerful evidence, I think) that they like the law as-is and want to see it applied to ban guns from parking lots. Of course there are many reasons a bill may fail, most of them more political than based on an honest assessment of a bill's merits, but.... it would still hurt us to try, and lose.
P.S. The Elk's Lodge case would not come out differently under your proposal. The youths were gathering in the parking lot while the older adults were gathering inside the building itself. Thus, there were two areas where people gathered, and thus both areas became off-limits.
Sporting events are particularly troublesome in this regard, because of all the "tailgating" going on in the parking lot. Ditto for music concerts where people "camp out" in the parking lot, grilling hamburgers, drinking, smoking, talking, etc. That's a public gathering in its own right.