If you are married to 12V, you are married to 12V. But you may find that an off-grid setup is more efficient of you can run the DC part at 24V, 36V or 48V. Higher voltage means smaller conductors, longer conductor runs, if needed, and less dangerous currents moving around. For 12V, you are just going to be paralleling up all your batteries, so the wiring you have is fine.
You do have three different battery types combined in your battery string: flooded, AGM and Gelled VRLA. I would wager that they are all different ages and conditions. This is definitely sub-optimal and will affect the overall performance. Especially, it will not be possible to equalize this string together. Estimating overall SOC will not be remotely accurate. One or two dodgy batteries could easily suck the life out of the good ones.
With so many batteries you will need a lot of fuses. If you do not have 100A fuse on each battery's (+) post, I do not want to hear about it.
I do not understand what you mean that you get only 600W from your 3,000W inverter. Why is that? Does it overheat or over-current shut down? or experience low input voltage or what? I would expect your battery string could supply 100A for at least a few minutes.
Battery University is a good place to read about batteries. They have a lot of stuff on Lead-Acid: http://batteryuniversity.com/
Also have a look at all the alternative energy and off-grid forums. There's a lot of good info about the ins and outs of battery system design and care and feeding.