Anywhere you have an RLC network, immediately think of the quantities:
Fo = 1 / (2 pi sqrt(L C ))
Zo = sqrt(L / C)
Q = Zo / R (series resonant) or R / Zo (parallel resonant)
If you want to dampen ringing, get Q down to or below 1.
If you want to minimize peak voltages, reduce Zo.
If you want to minimize peak currents, increase Zo.
If you want to shorten the pulse, increase Fo. (Including making it shorter than any relevant harmonics generated by the circuit, in which case Zo and Q matter less and less, in proportion to the range Fo is above those harmonics.)
Relevant harmonics correspond to the switching edge rate, whatever that is. You haven't posted a zoomed drain voltage or source current waveform, I don't know, you'll have to measure that.
I don't see explicit parasitics on your schematic; apparently, some of your models have them built in. You'll have to check which, and by how much. Look up how to view model source or whatever, it should be a dialog somewhere, or in a library file (unless it's encrypted, in which case you can thank LT). Or at worst, set up a test jig and measure it.
Conversely, anything you have, that isn't modeling parasitics, is probably erroneous. A rough estimate for stray inductance is 1nH per mm of trace or wire length. You'll need a rough or estimated layout to add these in.
Applies to component body length just as well. So a long film capacitor does worse than a short ceramic chip capacitor; though the film cap probably has a larger value, so there's that, too.
You can always increase capacitance or inductance, by placing components in parallel or series; you can never reduce them below the limits of the physical components, their dimensions and geometry. So, if thermal dissipation isn't a problem, PDSO-8 is better than DPAK is better than TO-220, for example.
Output ripple is the rectified inductor current, dropped across the capacitors. Just use better ones -- lower ESR and ESL. Electrolytics tend to need to be rather large (100s uF?) to get low values; they're cheap enough that it's not a bad deal.
If a single block of capacitors still isn't good enough (less than a volt pk-pk should be reasonable to achieve), just add an LC.
And, what values? -- well what did we just learn about RLC circuits? In this case, the output filter values depend on how much load transient response you can tolerate. Roughly speaking, Zo equals Vpk / Ipk in the transient response. You need Fo somewhat lower than Fsw, by how much depends on requirements. You may find ESR is actually desirable here, because if the load is not a resistor (or not equal to Zo, in any case), it'll keep on ringing. ESR provides damping for the filter (keeps Q low), independent of load (well, for RL > Zo; for RL << Zo (a shorted load) it's a different case, but maybe not an important one, either).
Tim