I'm going to address the larger issue of making the system robust and reliable, rather than just focusing on the batteries. The main issues that I see are: ruggedness, waterproofness, battery/charging, and the "chassis".
If I were building these things myself, I would use PVC pipe as the chassis. But more on this in a moment.
To increase ruggedness, I would encase the PCB in "casting resin". Just google "casting resin". Essentially it is an epoxy that you can pour into the PVC pipe to encase the PCB's to both waterproof them and support the PCB against shock and vibration. Casting resin is available from many hobby/craft stores like Michaels and Hobby Lobby. Just put your electronics in the PVC pipe, mix up the resin, and pour it into the pipe. Important Note: casting resin comes in 2 parts and the ratio of the two parts effects how long it takes to harden. The faster it hardens the HOTTER it gets during the curing process. You want it to harden as slowly as possible, otherwise it might get hot enough to damage the electronics. Experimentation with the resin is important to getting this right.
Casting resin will work best if your batteries are rechargeable and fully encased in the resin. However, I wouldn't do that. Batteries behave weirdly when charged. Best case your batteries could get hot and not be able do dissipate the heat due to the resin. Worst case, your batteries build up some internal pressure that can't be dealt with due to being encased. As an alternative, you could use some super-capacitors. The usefulness of super-caps will depend on your power consumption and a variety of other issues, but I've used them for several applications and they work quite nicely. Essentially, supercaps behave like rechargeable batteries except that they don't hold as much power but they can be charged and discharged almost an unlimited number of times.
If you can't use supercaps, then rechargeable batteries with tabs/pins/wires already attached would be your 2nd best choice. 3rd choice would be standard or rechargeable AA's. With AA's, I personally wouldn't spend much time making the spring keep good contact. That is a massive waste of time because whatever you do, it won't be good enough! Instead, your design should take that into account. The best way to do this is to simply put large-ish caps in your circuit so that if the batteries do momentarily loose contact then the circuit will remain powered up.
If you use supercaps or rechargeable batteries then next comes the charging system. You could simply have a connector that goes to a charger. Of course that isn't very waterproof. A cool way would be to have a non-contact inductive charger. Imagine a transformer with two coils of wire. AC goes into one coil and comes out the other coil. An inductive charger is the same, except that one coil is in the base of your baton and the other coil is in the "charging station".
In the best case everything-- including super caps, charging coil, and PCB's-- could be encased in casting resin. With no seams there is no way for water to get into the circuitry! And with everything encased and fully supported the whole thing is very mechanically robust. With a little bit of work, you wouldn't even need end-caps on the PVC pipe. That way your baton would be a simple and smooth rod. I'd bet that you could take this and throw it out of a low-flying plane and it would survive.
Also, Casting resin is water-clear. Your circuit can have status LED's that can be seen through the resin.
The PCB has two layers: top and bottom. They can be connected to each other using "vias", which are holes drilled through the board and then plated with metal. It's like running a wire through the board.
An example is the "MC+" connection to the right of your first photo. There is a rectangle of copper, which is partially covered by the green soldermask. The uncovered part is where the solder connection is made. If you look through the translucent green soldermask, you will see the vias.
So, now, if you inspect both sides of the board you should be able to see the copper current-carrying paths under the green soldermask, connecting from one side to the other with vias..
Does this help?
Best Answer
Magnets. Solder the power connections to the magnets. It will stick to most battery contacts.
I made some with a wood dowel (well, squared) and some copper. Cut to size and shaped to fit in the recess for the battery contact. I added a diode on one and usb connector so I could power a battery led string from usb. (4.3V instead of the new batteries 4.8V).
You could make a small shim from double sided copper clad board. If you cut or etch the copper to shape, you could use a pair of alligator clips on it. It goes between the contact and the battery.