romanlutsk, I will try and answer your points in order.
If you read the USB 2 specifications - all 30 odd documents - you will find there are two current specs. 0.5A for computer USB sockets and 1A for USB charging devices. What you need is the 12v equivalent of your 5v box - one that has a set of plug tips so you can get the right one for your PE.
With two batteries connected together each will try and take as much charge as they can - the only limit being the charging circuit and if the battery with the battery state circuit in nearly discharged the circuit will cut all restrictions as to current and with two batteries drawing as much current as they can something is going to get very hot and burn out. There is also a down side to low rate charging of batteries, it can destroy them by chemical contamination/change. We have had to change several batteries in clients laptops because they kept the battery installed and constantly used them running off the mains power supply.
It is good that you have a source of parts, something very few of have. I would suggest using the one with the WSoD to charge its battery and the battery of the unit with the dead charging circuit, then remove them and store them in a cool dry place. That way they will have a very reasonable life expectancy.
A question. You are looking for ways to power your PE, what is wrong with the mains power supply that came with it, or are you away from mains power for long periods as well?
My comment to tarvoke, was that unlike professional grade equipment the EE and PE were built down to a 'it just works' standard as several people found out when they tried to push the operation of, mainly, the video circuit beyond its capability resulting in the WSoD because sections of the video chip were fried. The only way you will increase battery drain to any extent is to be in a WiFi fringe area - WiFi increases the power output to connect, or try and increase the clock rate of the processor and there you will see increased power drain and heating.
I have to admit I am at a bit of a loss as to why you are thinking to do what you describe because I find it strange in this day and age that anyone would be out of reach of mains power for any length of time.
We have one client that has a house in the mountains that doesn't have mains power connected but he uses all his mobile devices and laptop there without problems - we supplied him with a ups powered by a large car battery he only has to remember to bring the battery down the mountain with him and charge it for the next time he goes up to the house. If you are in that situation matbe somethinf like that would work for you.