<< Maybe I'm off base here, but don't certified aircraft have to be controllable at the trim limits? >>

Nope.  It's perfectly okay for a certified airplane to be uncontrollable with a trim which runs away all the way to the stop.

The FAA only requires that the aircraft remain controllable "following any probable powered trim system runaway that reasonably might be expected in service, allowing for appropriate time delay after pilot recognition of the trim system runaway."  For those who care, this is in CFR 23.677 (d).

In practice, the FAA says that three seconds is an appropriate time delay.  So the trim runs away for three seconds before the test pilot is allowed to take corrective action, which is generally to hit the quickly-accessible cutoff switch rather than dig around for a circuit breaker in the middle of a sea of breakers.  Then he demonstrates that he can fly and land without exceeding control stick sustained force limits. 

The trim rates that engineers select are therefore a balance between the Part 23 requirement to be able to land using trim only (you want a fast rate for that) and the ability to withstand a three-second trim runaway (you want a slow rate for that).  You are also forbidden by CFR 23.1309 (systems safety) to have a single point failure which result in a hazardous condition, thus if a runaway trim is hazardous (and it often is) then that's where the doubled up switches come from.

Just one more example of what's behind the curtain at a certified airplane factory....

- Rob Wolf