So one of the things I liked about the Solo was the fly time usually around 25 minutes per battery before Gimbal. Now that I have the Gimbal I'm down to less than 15 minutes and that seems to be because it charges the GoPro at the same time.
Soooo
Pro's: Don't have to worry about charing my GoPro I have a back up energy supply

Con's Less Fly time more finding GPS time

Pro's I can see the live feed from my GoPro

Con's But the HDMI has yet to work correctly

Pro's During a wedding I have to change battery's in the Solo but not my GoPro
Con's I can't stay airborn long enough for most weddings these days

Pro's The Gimbal does a decent job of filming smooth
Con's My editing software did a good job of stabilizing the video before Gimbal, need more battery power
So post your pro and con on the evolution of the battery decline.
Not sure why you are having such short flight times, but that is not me experience, and I am certain it isn't the GoPro. I haven't checked electrically, but the Solo provides just enough power to keep the GoPro going. If mine isn't chnarged up, it shows charging, but doesn't noticeably gain charge.
That tells me it also isn't drainng Sollo appreciably. My experience with the gimbal is about 20 minutes flight time, when i was getting 23 minutes before w/o gimbal but with camera. Obvioulsy this depends on flying style, but I am low and slow when filming. In distance tests when I was trying to go out far and fast, I got 17 mintes. Shorter with the gimbal certainly, but about what I expected...
Also not sure why your HDMI doesn't work? I use it with an external monitor and it has never not worked for me. if you have live feed, I can see no reason why this won't work, as video is making it to the controller. Getting it out of the HDMI port on the controller is trivial from there. What is the symptom of the problem? Have you started a ticket?
I did the GPS cardboard mod (I actually used the gel) and since then, I get a lock in less time than it takes me to get set up, and far less than it takes for my P3 IMU to "warm up". I even get a GPS lock in my house now, which is scary... Have you added the insulation on top of the GPS?
I just did a wedding. (though I normally don't).. Not sure why you can't do this even with 15 minutes if you have multiple batteries (I have 7) and I am confident could work withy 10 minutes if I had to. That said, I think something is wrong with your setup.
My experience with some of the best stabilization in the business (Premiere Pro, etc.) is spotty. It works well in certain environments (short clips with fairly constant backgrounds and lots of framing space around the shot) and not so good in other complex or tight shots with changing features. I use it where needed, but I don't count on it to fix everything. It also won't "tilt" up and down for you as the gimbal does, which is a MAJOR feature of any gimbal, including this one...
The other thing not covered is the integration of the gimbal with the smart shots. The way they did the Smart Shots, the gimbal will move (in addition to the bird) with a smart shot, and that is a real game changer if you are filming. Not sure if you have used this, but you really should. It is PERFECT for things like weddings, and gives you ability nobody else can compare with using automation and one pilot. I wish I could show my footage from yesterday, as it tells a thousand words, but I don't own it. Suffice it to say though that the bride/groom coming down the isle with Cable Cams was awesome, and the "Selfie" off the bride and groom after the kiss was "panoramic". Their reaction just looking at raw (silent) footage was "Oh My God.. I can't believe you did that"
And for me... It was simple. I was actually taking stills while it was happening... :0
My 2 cents
Cheers