Should I select components based on peak current, RMS current, or average current?
In short you need to choose the part to survive the peak current.

Longer Answer: 

I'd work your way through the SEPIC topology's design calculations again, your current ripple is really high, the difference between average and peak current should be much smaller.

The datasheet says that ΔIsw should be 20-40% of Isw(average max).  Or to use the datasheet's terminology χ should be between 0.2 and 0.4.

In your case (estimating by looking at the simulation output graph):

Isw(average max) = ~2.75A

ΔIsw = ~5.5A

χ = ~2.0

Try rerunning your simulation with larger L1/L2 inductors, this should reduce the ripple currents.

EDIT: try a larger cap for C3 also (try 10uf or a second 4.7uf in parrellel), the ESR / ESL of this part is also critical, check what the values of these are for your simulation model.