Your post covers several major topics.
On the GFSZA, there have been several threads, some even rather recently on this subject. It is easily one of the most vile and universally hated laws among law-abiding gun owners in the country, at least the ones who know about it and what it really means.
As the wiki article suggests, I strongly believe that the law makes it almost literally impossible for a "non-permitted" person to legally carry a gun in any urban or suburban area in the United States.
I also strongly disagree with the opinion of the BATF which states that the permit must be issued by the home state. A permit is a license, which is a non-tangible status of being, not a piece of paper or a card. If Virginia recognizes an out-of-state permit for me to carry concealed, then it is Virginia that is "licensing" me to carry concealed (in deference to Virginia's laws), based on the status granted by that other state. Who did the background check, and mailed me the piece of paper that documents this status of license is not relevant.
Of course, I am not a lawyer, and as previously posted, I would not go looking for the opportunity to test my opinion in court either.
As far as qualifications for the CHP, you are correct, you may not be eligible at this time, depending on how long ago your DIP charge took place.
You can look up the requirements and the disqualifications for a Virginia CHP here. Go ahead and bookmark that page, I'm sure most of the rest of us have already.
Scroll down to Paragraph E. 9, which is the section on DIP:
9. An individual who has been convicted of a violation of § 18.2-266 or a substantially similar local ordinance, or of public drunkenness, or of a substantially similar offense under the laws of any other state, the District of Columbia, the United States, or its territories within the three-year period immediately preceding the application, or who is a habitual drunkard as determined pursuant to § 4.1-333.
So you may be eligible soon, all depending on how long ago it happened.