For the airline tickets, where are all of the points on the AMEX coming from? Somebody must be charging on the card. Assuming there are others who are using the card, are you the only person in the company traveling? Why do you have to take all of the free tickets? Maybe you can negotiate to distribute the free tickets with others in the company.
In line with previous comments, the company should also consider the cost of the miles versus the price of the ticket. Maybe you can negotiate the purchase of an airline club, which can replace some of the elite status benefits depending upon the airline and make the business travel tolerable without the airline status.

Good luck