well, concerning the noise I guess it will be a suck it and see scenario.
Concerning the Lipo, in my opinion, based on the fact that you need it to transmit for a loooong time, I imagine that you can sacrifice the LIPO in order to get a few more days of transmition, I assume the price of a dead LIPO isnt significant when compared to getting more data,
That in mind, a LIPO normally goes down to 3.2v, you should do some testing with the ones you decide to use, but if you take it down to 2.5v I dont think it will set on fire, maybe a small swell. BUT at that point you should be able to decide if you want just a little more transitting power, or to stop and shut off, you will need a voltage measuring circuit on the arduino, and the ability to shut it all off if the battery goes critical,
now I think about it ,
http://www.ebay.com/itm/2-PANASONIC-NCR18650B-LI-ION-BATTERY-3400mAh-3-7v-18650-NEW-PROTECTION-PCB-JAPAN-/370925377492if you can get a couple fo these badboys in there, even just one, you should have plenty of power. They can go down to lower voltages, but IF they get over discharged, they can literally go off like rockets, so it needs to be considered.