Depending upon your workplace, maybe you can negotiate a deal whereby you get the business class ticket with your miles, but only expense a regular one (premium if possible). Some accounting/auditing departments have a bit of sense and will work with one. Back when I was working, my company sometimes did.

For that matter, it isn't unusual for companies to let employees travel business class for overseas trips. Might be where the "business" part of the name came from?

Otherwise, guess you are just going to have to suck it up in the back of the plane. BUT, you will be earning lots more miles, and can ultimately use them for your personal travels. Just don't let any of them expire!