The current requirements of the RPI and the Arduino are at two different ends of the spectrum, therefore if you do not want to consider different battery types for either then there will be a big compromise optimising the weight & power.
Without specifying what your project is (why the secrecy?) it is hard to get a handle on what you require. 'Mobility' for your project could mean anything from the device embedded in your clothes to one sitting in your car/boat/mower etc. If mobility is not critical and you need to run this thing for more than 1-2 hours without charging, you may want to consider using a 12v 7.2 AH gel-cell battery like those in alarm systems. Heavy but can deliver the grunt required for a project that with all parts included may be pulling >800 ma. There is no memory effect either.
The problem with running LiPos in series is highlighted in the previous post but running NiMh in series can result in balancing problems and memory effect problems over time.
I know that you don't like Li* batteries but I have used over 20 of these:
coupled with these:
to provide a safe charging solution with a stable 5 or 3.3v (selectable) irrespective of the charge state of the battery. You would need two for the current needs of your project or use separate, high current buck-boost converter.
These setups have had not had any failures or meltdowns to date.
By using a single cell the danger highlighted by the previous comment "If one cell is damaged, or its voltage falls below the voltage of the other cells, the other cells can discharge rapidly into it and cause a fire" is obviated.
P.S. the parts listed above have very cheap postage if you do not select express options. Where do you live? The South Pole?