What about the ongoing cost of waste and eventual cost of decommissioning? Are those affected by quantity of fuel used (or, more specifically, by Transatomic's design)?
When a reactor is built in the US, the operator will start paying into an account for waste disposal. This is included in the cost of energy production. Since high level waste quantities are pretty low for nuclear reactors (About 27 tons a year)[1] disposal of fuel isn't the largest issue.
Decommissioning on the other hand is remarkably expensive because of secondary nuclear waste like contaminated reactor vessels and concrete make up 99% of the nuclear waste.
