milesandpoints: I can empathize with your situation. My employer has the same policy with UA, DL, TW, and US. However, there is a loop-hole that may also exist for you.
If we choose a route with a connection, it is compared with a route with a connection within one hour on the preferred airlines. The same comparison is made for non-stop. IF you play it right, you can always find a CO/HP/NW/AS route that is cheaper. Just an idea for you.
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The only difference between ordinary service and extraordinary service is a little EXTRA.
-- Bob