I wont recommend Lead acid for this application
cause u can ruin them on deep discharges
NIMH would be a better application as u can
build a 5 cell 6 volt battery pack with 3 AH AA
cells and it take far more cycles and deeper discharge
Only reason I use them for lighting is emergency lighting and I use a Low voltage drop out regulator.
The deep discharge is not hurting that much (compare to other chemistries), if it is for short time only. It is even more robust against over discharge than NiMh and if kept on float voltage charger, it remains ready all the time without degrading like LiIons use to do (so ideal for something resting on a maintenance charger occassionally pulled for iuse and returned back). Up to now, the lead acid (in any form) is still the most robust technology (temperature range, discharge currents, short term complete discharge,...), when kept charged during normal storage. Plus they still offer the lowest cost per Wh...
Personally I would stay away from the 3Ah or higher capacity HR6 (aka "AA" size NiMh), they have no reserve at all for any abnormal operation (overcharge, over discharge), yielding to premature aging (demonstrating as increase of internal impedance).
Better to use the 2Ah "ReadyToUse" types (Eneloop,...; very cheap sold as Ikea Ladda). Even when on paper the capacity seems to be not that high, these tend to maintain it really with very wide range of loads, unlike the "standards", which tend to loose it after few cycles at elevated current.
An undervoltage (underdischarge) protection is a must with these, otherwise the cycle life will drop significantly due to electrode corrosion (accelerates when cell voltage drops below about 0.9V).
LiIons dont like to be stored fully charged (their degradation accelerates at voltages above 3.9V), but unlike others they do not wear on charge/discharge cycles at all, so they are perfect for just permanent cycling use (discharged by working with the machine, recharged, then discharged again and over and over). Dont think that fits the application. But today seems to be the second cheapest per Wh, but need precission voltage charger and active protection circuit for safe operation. But all that electronic is readily available for cheap, so still seems to me as the cheap way for a 10Wh range (that is the single 18650) battery.