Ehhhhhhh... please don't increase the gate resistors. They're probably marginal as-is, and with poorly chosen, antiquated transistors, the rise time was probably pretty nasty to begin with.
That said, it doesn't look like much heatsinking, so maybe the switching design wasn't too terrible. Which makes worsening it all the more dangerous. If nothing else, don't call it "done" until you've done a full load test (elevated ambient temperature, various load conditions including full rated current at low voltage, half and full voltage). Keep spare transistors (and whatever's in the gate drive circuit) handy.
You should be able to identify what loops are ringing. This is the kind of thing you can track down piece by piece: squash one squiggle, find the next largest one, and so on. A near-field probe (E or H) is good for this. H probe can be a small coil of wire, insulated: wave it around the circuit and see where signals peak, and rotate its axis to test directionality (it's sensitive to currents flowing along the turns in the coil, which is the same as saying, magnetic fields parallel to the coil's axis, because currents produce perpendicular fields). Fields are gently curved and fade gradually, so you can track sources by the relative intensities and wave shapes near different components.
Ferrite beads may not do very much, because they saturate quite easily, and can actually make other things worse (increasing overshoot or reducing damping in the power supply network). Ditto bypass caps (or both). It's worth some back-of-the-envelope numbers to determine whether what you're adding will affect these or not... or do anything at all.
That said, it still seems likely that adding a ferrite bead to the offending node (I would guess it was diode reverse recovery..?) would still help, because of two effects: the remaining impedance (even when saturated), which won't be too bad at 80MHz (~10s of ohms, probably comparable to the circuit's impedance there, thus damping it, or shifting it down at least), and using the saturation as a feature rather than a bug: when a ferrite bead is saturated, it acts like a hunk of wire, but as it comes out of saturation, it absorbs a big gulp of flux (volts * time), which softens the blow to the diode and makes reverse recovery softer. Once the diode is off, the ferrite bead isn't carrying current either, and it resumes its ferrite-beaded glory, dramatically increasing the inductance (and loss) in the diode's loop, damping oscillation versus the diode's capacitance.
Ferrite beads are also commonly seen on transistors, usually the input (base/gate) or common (emitter/source) terminals, or both. I wouldn't recommend the latter, because again, it's probably not going to do much (that's where load current goes). But there can be value in the former, especially if there is pressure to keep gate resistance minimal (for fastest switching).
What happens there is, if there's a big beefy gate driver chip, it can deliver such a jolt to the gate that it momentarily saturates the series ferrite bead, so after a short delay (less than 10ns?), the gate swings as quickly as ever, and as gate voltage comes to a rest (damped by circuit resistance), it comes out of saturation and resumes being a higher impedance, damping possible gate oscillations.
Don't forget to check common mode as well as differential. If your probed measurement changes whether there's a ferrite bead on the probe cable or not, suspect everything!
Good luck,
Tim
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