Thank you for the advice, unfortunately, I have tried turning off the vehicle's "God" mode to no avail. The only thing that stops almost all of this issue is to lower the vehicle's mass to its default value, but then you can't smash through things. I am not using ENT, instead opting to use Simple Trainer (https://www.gta5-mods.com/scripts/simple-trainer-for-gtav) so that might be something for me to try out and see if there's any issues.
I have tried lowering the center of mass for the Z-axis and while it has some effect, I have the traction turned up so far that it will likely always go up on 2 wheels when cornering while not using Franklin's ability. On that note, however, I have found that increasing the Z-axis for the inertia multiplier helps curtail a very significant amount of that cornering issue.
Thank you again for the advice, I'm going to try out ENT and see what happens there.