I have miles I'd like to use for either business class or first class, but the work requires a few things for reimbursements

1) they will reimburse economy
2) they will reimburse whatever dollar amount appears on the e-ticket

Given these constraints, how can I get the work to reimburse me for economy price, while riding in business or first?
Which airline will allow me to do this?

As far as I can tell, I can either purchase a full price economy and upgrade using miles, or book a flight in economy or J/F using miles and somehow try to get partial reimbursement, but that will only work if some dollar amount appears on the e-ticket.
I don't know if the partial reimbursement will work if the dollar amount is for the J/F ticket, rather than Y.