First of all I never was convicted for the A&B on a cop. I took a CWOF once I completed probation the charges were dropped against me. It would be one thing if I was convicted therefore I was not convicted.
Doesn't matter. The chief of police has almost total discretion in the issuing of an LTC. He can issue you an LTC if he wants to. He can deny you an LTC if he wants to. And there is very little you can do about it.
If you decide to go forward with an application for an LTC, you should contact a competent firearms attorney to maximize your chances of success. Realize, however, that even with the help of someone like Darius Arbabi, your chances of success are slim.
Given your attitude about the issue -- it didn't happen, the cops lied, etc. --, I'd say you have zero chance of success. If you accepted responsibility for what happened and were contrite about it, you might be able to demonstrate to the licensing officer that you have grown up and turned your life around. If you tell the licensing officer that the cops lied, you won't get an LTC.