I don't find the mentioned aspects of "First Duty" impausible at all. You don't need to establish coordinates when you always know that one end of the process is the pilot's seat and the other is the evac station at Mimas. Indeed, the seat is probably a "transport seat" the same way modern aircraft have an "ejection seat". The actual transporting machinery would still lie at Mimas and would not be lost when the craft was; once the pilot started sparkling, he'd be safe and sound, phased out of this universe, impervious to the explosion of his craft from around him (we've seen people getting shot at and shot through when sparkling, and they survive just fine - see ST6 for example).
What's a bit iffy about "First Duty" is the distance across which the transporter is implied to work. The traiing craft collide at what they call the Titan flight range, and are rescued by transporters at Mimas. The distance between those two moons of Saturn is always about a million kilometer at least, while starship transporters sometimes appear to have a maximum range of mere tens of thousands of kilometers. But fixed installations might be more capable, and the whole Titan flight range might be chock full of "pattern enhancers" or whatnot. It would be designed specifically for safety, after all; if instant surefire transporter rescue weren't possible, then I'd think something was not written particularly well...
Timo Saloniemi