I did some more searching and discovered that this problem is much broader than Model:Cycles. It seems that it effects most Elektron machines in varying amounts, some having more successful workaround than others.
This comment from another thread does a good job summing it up:
That thread started more than six years ago so I’m not gonna get my hopes up that this will ever be fixed.
Pretty absurd to me that Program Change is so functionally useless in Model:Cycles as well as many other Elektron boxes 