you could get two cathedrals and run them in parallel, alternating which you’re infinite-sustaining on so you don’t activate the tap tempo.

From a more budget minded perspective, have you considered any of the old digital delay pedals like the DOD DFX9 (digital delay)/DOD DFX91 (or DFX94) digital delay/sampler, or even a Digitech RDS rack? setting the repeat rate really short and putting one of these in ‘repeat hold’ mode is pretty similar to the freeze (and can arguably be called the predecessor to the grain synth technology of the Freeze/SuperEgo.)

Basically you’d be making super short loops – maybe 12-20ms – and tapping them again to turn the loops off (they’ll die off in accordance with where your “repeats” knob is – more repeats, longer fades). These can be picked up for around $40-120USD on ebay. The RDS racks, you’d need separate footswitches for on/off and repeat hold, but you’d also have the option of using momentary footswitches, which would be nearly identical to the freeze’s non-latch modes. This is what I use my DFX9 on my synth for (that and quickly changing the release value for when I need longer string fills.) The cheaper models of the RDS units are going to be the 900, the 1900, the 3.6, and the 1.8.