LiFePO4 is less dense than LiPoly, so not much better than 2500 mAH NiMH. The reasons for LiFePO4 vs lipoly/Liion are:
Cheaper on large packs.
Less fire risk on vehicles and solar.
3000 to 4000 deep cycles (so about x3 to x5 life of lead acid on solar
Less toxic / more recyclable (but lead acid is 100% recycled except case, which could be renewable) than LiPoly/LiIon.
So the advantage of LiFePO4 is for external packs of 9 Ah or more rather than short-lived heavy Lead-acid gel packs (was 7, now 9 Ah).
For occasional use the long life quality low discharge 2500 mAh NiMH is best internal and longer operation at full 5W with an external LiFePO4 pack (you want minimum 9.5V, max 16V, but a nominal 12V is about 11.5 to 14.5 for min-max). One with internal BMS to disconnect when too low and allows usually 2 to 4 in parallel is best. There are 3rd party LiFePO4 chargers.
Otherwise a replacement Wincamp, but external LiFePO4 (DC House brand seems OK and ecoworthy is same company). Search Amazon etc for LiFePO4 10Ah. Make sure any mains charger compatible with the Ah rating and for LiFePO4. Max fast charge current is typically 1/2 the total Ah rating. You can't use a lead-acid or LiPoly/LiIon charger unless it has a switch for LiFePO4.
Mike EI9FEB