Retrolefty, based on my experience with the DOE test procedure I do not agree with your position. It is not a closed system. So if you can control the flue exit temperature of the drum, you should be able to reduce the amount of energy needed to dry the clothes. In the beginning of the cycle, you'll be able to run full bore because the clothes are cold and wet. Beyond a certain temperature, the marginal improvement of full heat vs. modulating will become apparent. Whether that justifies the extra expense of a SSR-based PID-enabled control system is a different question.
Similarly, increasing the drying cycle time will likely reduce your need for heat by using "dry" ambient air - for flue-based dryers, the test procedure does not account for the inherent issues in using air from inside the house and then exhausting it. Yet, in real life, that air has to come from somewhere, i.e. it will cause infiltration. Said infiltration is going to impact the home in one way or the other. BTW, there are no 'balanced' flue-based dryers on the market - i.e. all of them source indoor air and exhaust it outdoors.
As for condensing dryers, all of them are based on electric power and are generally less efficient than their non-condensing platforms. The sole exception here being heat pump dryers marketed by Bosch and others in the EU, but not the US (at least, not yet).
I agree with you that measuring dryness of clothes is the best way to ensure good process control, regardless of the control mechanism being used. However, should you find yourself with not enough to do, have a look at the many different ways that people have tried to figure out clothing dryness inside a dryer.
Now a quick suggestion for the OP: Before you rip out the old control system, etc. may I suggest you install all the sensors we talked about and then log the different behaviors of the control system. That gives you a baseline to compare your dryer performance / algorithms to. Just a thought.