Bryan,
I prepare my own timber. I buy in seasoned rough saw timber. The elm came from Whitney Saw Mill, just out side Hay-on-Wye.
You will be very fortunate, indeed, to find a commercial saw mill that will cut and prepare 6.5mm timber. There are a number of reasons why :- Cost, time, and complete customer dissatisfaction. Very thin timber is unstable, some more than others. Beech, I think is the worse, African hard woods seam less affected. I use elm because it is the most stable of British hardwoods.
Also a lot of commercial mills use four sided planers, and thin wood will not be able to stand the machining. Another factor is the ratio of waste to finished material. For thin timber it is disproportionately large. There is a lot of shavings and saw dust going up the chute.
Not really of much help.