5.9A ripple is within reason. It'll depend on the duty cycle and inductor current ripple.
Moving to an interleaved design would reduce the ripple quite a bit, but needs more parts.
There are 4 capacitor options:
1) electrolytic. Has ageing and operating temperature concerns.
2) many ceramics in parallel. Beware the fact that capacitanc drops a lot with DC voltage.
3) film capacitors can be excellent but are normally through hole
4) tantalum caps can be very effective but need to be de-rated in voltage so they don't catch fire or worse.
Be aware that current can flow from the battery, through the inductor, through the upper diode and into a short-circuited output. The control IC can't stop this, so protection (maybe a fuse) should perhaps be deployed.