Transferring is always a concern, but I harken back to what I say every time when it comes to QBs: what high end program could he go to where he is guaranteed a better shot at PT than he has at Iowa? There is competition everywhere, and unless he drops down a couple tiers, no one is handing the reigns to a kid who has not taken a snap since high school. He would have to show up, compete, and be the best QB on the team.
Let's assume Heck wins the job and keeps it all year. Brown likely transfers. Bessinger ascends to the back-up role and is slotted there for the next two seasons. He would still have 2 years as the starter after Heck runs out of years, and he would be one hit away from getting on the field as the backup to an undersized QB who likes to scramble.