A couple of suggestions! You do very very nice building, far better than I can do.
After some iterations of homebrewing, Ive found you can't beat the cost of the "Frog Sounds" QRP kits that the various chinese suppliers produce . You ccan modify the LPF on them and ditch the receiver section and end up with a half watt output transmitter, board and all parts (minus the crystal of your choice) for about $2.99 if you buy 10 at a time and shop carefully. Yes, the LPF is using inefficient chokes rather than toroids, etc but..... you can substitute if you wish.
As far as a micro goes, the Nano is what I started with too. Then I found the ATTiny85 which is way more power efficient and ...well...tiny. There's some libraries out there that sleep it at under a mA. There's still enough pins left over to say...(hypothetically) turn the DC bias OFF to the transmitter (no use powering that voltage divider if the transmitter is off) take battery measurements, and convert to a morse string, etc etc. and have space left over for other fun things (like high side and low side switches).
I've experimented with the charge controllers that are available (also Pride of China) and they work well. I still use a LDO 5V regulator (to-92) for the regulation from the battery to the Tiny, but they're pretty efficient. When the Tiny is in sleep mode, there's not much load to warm up even that tiny regulator. I use the full battery voltage to the transmitter. Jim's suggestion on those little battery charge boards is a good one.
Hope those help!