Zeek
The alpha case is a byproduct of oxygen and nitrogen making oxide and nitride layers that increase in thickness with temperatures over 800F and also are related to dwell times at temperature.
You need to tell us a bit more about your furnace cycle.
Vacuume?
Argon?
Air?
If you are wrapping in foil and cooking the thing in air you will have alpha case no matter what you wrap with... You will need to focus on the best methods to remove the alpha case.
Here is a good link to some data on stress relief of 6-4 Ti
http://www.timet.com/6-4thermaltreat.htmlFor more detailed information consult ASM Materials Properties Handbook Vol 4 'Titanium Alloys'