I have read all the comments, and want to add my 2 cents, because I came here hoping for a solution, but the solution appears to be "that is just the way it is". And, if a slightly slower charge helps maintain the battery life, all the better.
1. As far as Verizon/Apple Lightning connectors, I purchased a mini and a New iPad from the Apple Store, and both came with the "squarer" lightning connector, so I don't think that the connector is the issue.
2. Charging time -- I noticed that the charge time is slower on the New iPad than it is on an original iPad, or any iPhone. If the battery is larger, than so be it. I get this.
3. The odd part, I suppose, is that if my New iPad is at a 75% (randomly chosen) charge level, and I have it plugged into my MacbookPro (with retina, so newer), and the MBP is also plugged into the wall...if the New iPad is On (screen is on, no apps running), it actually doesn't seem to ever get more charged -- I actually think it does, but at a *really* slow rate, like maybe 1 percent more charge every 30 minutes or so. But, if I just turn off the device, it charges at its "normal" charge rate.
And, yes, charging overnight is obviously a good idea, but I use this device all the time, and put it in my work bag, so at times I forget.