Yes, I did mean that you can shape the envelope before it ever gets to the synth.  To get your short envelope, it might be easiest to first try out TremoloPan into PolySynth in Series.  [You can also try out Manual / Manual Mod with your expression pedal here, instead of Env / ADSR as the Shape (below)]:

• Depth – up full
• Adjust Speed / Sensitivity after selecting …
• … Shape to Env or ADSR
• Width – 0
• The remaining controls to 0, or to taste.

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The one I use most often is a little trickier to dial in:  UltraTap into PolySynth in Series.

• Mix – 100%
• Length – 0 mS
• Taps – 1
• Pre Delay, Spread, Taper, Feedback, Tone, Slurm – all at 0
• Chop – Trigger or Swell adjust between 0-9
• Speed/ Rise / Release – the decay time of Trigger, or the Attack time of Swell.
• Width – 0

Bottom Line:  You are just using the “Chop Machine” section in UltraTap.  Tricker because crossing the threshold of Trigger or Swell takes some fine adjustment  of 0-9 to get the most consistent results.  And it also depends on your input note levels.  A compressor on your bass beforehand might help out there.  Also, mix in any of the original signal with the Program Mix control.  Everything else will be 100% wet in Series.

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And yes, it would be simpler with an ADSR in the synths themselves, but I’m all about working with what you currently have.  PolySynth has me going back to revisit HotSawz for similar effects.

One more option just might be going external, with another pedal as Inserts before your H90 synth of choice.  I use a Poly Effects Beebo for this, and have used a Pigtronix Philosopher King as well.  Seems like the reissue EHX Attack Decay would be a perfect choice here (the rare original I have here is far too noisy).