I think I was able to recreate the lead from the first track in Spire. Osc 1 & 2 are at full volume, osc 1 is tuned up 12 cents, detune set to 690, density at 500, 7 voices. Osc 2 is tuned down 12 cents, detune at 690, density at 425. Both oscillators are at full width. Routed to an infecto filter with a bit of resonance. All that then runs through some soft distortion set at about 25% dry/wet, set the drive to taste. Set your delay and reverb and you should be good to go. The key with these types of saws is the detune between the oscillators, not just the detuning on the individual oscillators. I've found that by spreading your 2 oscillators by +-12 cents in this case it gives you a less harsh sound.

Layering multiple soft-synths (VST's) gives supersaw's a unique feel. Use presets and tweak to make brighter...adjust filter cutoff...detune...use reverb

Simpler than it seems.

Make a standard supersaw type thing, just two saw oscillators with some unison voices. Don't go overboard with the detuning. Give it a lowpass pluck, and automate the sustain.
Then duplicate it, transpose up one octave.

Add chorus, distortion, delay and reverb.

To get more of that huge, messy sound, try using a bit of vibrato and/or a phaser.