Seven degrees of divergence is about 1mm expansion in a length of 10mm. So if the part of the TP that is to be taper bored is say 3mm diameter and 3mm long then it will need to be opened out to 3.3mm dia at the exit. You're probably right, this is more than a taper reamer would give you.

How about turning a piece of silver steel with the desired taper, file it off to half diameter, harden and temper. Hey presto a D bit in no time.