Another trike user with 20" wheels all-round.
I run a different tyre on the back vs the front two but more to even the wear rate front to back.
I only really stress the front tyres in silly high speed corners/braking, while I stress the back tyre more often due to hill climbing.
With the same tyres front/back, I'll wear the back tyre out in half the time it takes me to wear the front ones out, ~4k vs ~8k.
I got a bit bored of trying to find a decent 20" tyre part way around a long tour.
So running a heavier duty tyre on the back gives me more rubber to wear away and all the tyres now last roughly the same distance.
Plus the heavier duty tyre gives me slightly better puncture resistance which is important as a back wheel puncture on a tadpole trike is a lot harder to fix vs a front wheel one.
Luck ........