I think that this statement is the heart of the problem. I'm assuming you were originally booked in Biz class due to the 14 hour rule. Someone at your agency spotted the booking and decided it would be more cost effective to fly you in coach. However, it should be entirely within your rights under the JTR to book in Biz if the flights total more than 14 hours of air time without a stopover.

My approach would be to tally all of the costs associated the Biz booking vs. the Coach booking + stopover (hotel costs, transport, per diem, etc.) and show them to your supervisor and travel department. Common sense does sometimes enter into government employee thinking