There are three other minor ways of getting Battery Packs that you might maybe have overlooked: Iridium Bats, special loot in Skull Cavern, and Pam & Kent's mail gifts.
Iridium Bats have a 5% chance of dropping a 'Pack upon death, doubled with a Burglar's Ring.
Special loot in Skull Cavern can be dropped from Crates (2.2% of Crates) and monsters (very rarely), of which 8% will be a Battery Pack.
Pam & Kent will randomly send you mail (very unreliably), which can give you a Battery Pack if you get lucky or you're okay – and patient – with reseting the day. With my experience, you'll need a combination of both! ;D
But unfortunately, I don't think any of these are "farmable" in the sense that batteries from Lightning Rods and Solar Panels are.
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@FilthyGorilla has some solid advice on how to get set up. For maximizing the potential, though, you have four options:
- Maxed Out Solar Panels – They are more expensive to craft, but give you a consistent, predictable stream of output, however they take much longer to process.
- A Thundery Approach – Lightning Rods the item are much cheaper, but they also require the infrastructure to give you Rain Totems. They are less consistent, and it relies on chance when you get the opportunity to refresh to "storm chain". Plus they're limited to the amount of Lightning that can strike in one day, which isn't particularly high. But since they can produce much faster with the right weather luck, you can get more batteries without the investment of hundreds of machines.
- Mixed Option #1 – You chain the storms when you get them, and have the Solar Panels to make the most of the gaps in the thunder cycle.
- Mixed Option #2 – Alternatively, you have the Lightning Rods to make the most of the unfortunate weather, and the Solar Panels are where your money's at.
If it was me, I'd probably go for Mixed Option #2, because it requires less time spent harvesting, Solar Panels can be placed off the Farm, and they're more expensive – which simply means more fun time spent in Skull Cavern! And only having to harvest them once a week would mean that I'd have the time to do properly deep runs.
Whichever way, Skull Cavern is going to be your best friend. You'll get Quartz, Iron, Gold, Coal, and Bat Wings all in one place. Plus you might get some bonus batteries from the Bats and Crates while you're there! :)
A left-field approach would be to farm hundreds (thousands?) of Fairy Roses (in Pot-Sheds) and Diamonds via Crystalariums. This would give you enough Fairy Dust to justify spamming it on Solar Panels, however you would need 7 Dust for 1 Battery, so maybe it's not such a great idea.
Whatever you do, I think this a really fun idea for a challenge farm, enjoy your run!