The bridge height doesn't seem excessive (have you seen the bridge height on a lot of Gibsons lately?), though lower is always better. Looks like you could bring the stop bar down a few turns.
Your bridge pickup doesn't appear to be that far away from the strings, so I can't see that being an issue for the guitar output being low. But I don't know anything about the stock pickups that come with the kit, and what output they should have.
My first inclination would be to go with Woks' suggestions, and look at the amount of relief in the neck, and then to check for one or two high frets. If you lower the action, do you get the strings starting to choke on all the frets, or is it only one or two that do it at first? If just one or two, then that indicates it's those frets that are slightly high and are preventing the overall action from coming down. If basically all the frets at the same time, then the frets are fine and it's mainly a neck angle issue.
Shimming the neck is an option, though it's normally done at the back of the neck pocket to increase the neck-break angle. You'd need to do it at the front of the neck pocket, which would leave a visible gap. In this case, one option would be to simply take off 2mm from the bottom of the neck heel so the whole neck sits lower in the pocket whilst keeping the same neck angle. A minimal amount of refinishing would be needed to the neck if you did this.
But before you do that, what's the action at the nut like? If the slots are higher than necessary, then that will be raising the action over the whole fingerboard with no strings fretted (but it doesn't affect the action of fretted strings). How big is the gap between the stings and the first fret? It should be just enough not to buzz on the fret, but low enough so that you can fret the string with very little force required to push the string down. It's normally a fraction of a mm, so any gap between string and 1st fret that looks higher than 1mm is certainly higher than it needs to be (unless you are setting up for slide playing, where a higher-cut nut can be useful). If undecided, can you take a picture?