Ben, I agree with the earlier poster that additional breakin may very well help. However, although most Tannoy speakers that I am familiar with have tube friendly impedance characteristics, unfortunately I suspect that the root cause of the problem in this case is that yours do not.
I suspect that the impedance curve of your XT6F speakers is similar to the one shown for the XT8F in the graph at the very end of this review
. As you'll see, the impedance of that speaker, despite its 8 ohm nominal rating, is around 3 ohms in much of the bass region, rising to around 10 ohms in the mid-range, followed by a sharp rise to more than 40 ohms at about 4 kHz, followed by a decrease to around 10 ohms in the upper treble.
As a zero feedback tube power amp, your PrimaLuna undoubtedly has a fairly high output impedance, corresponding to a very low damping factor, although neither parameter appears to be specified. The interaction of a high amplifier output impedance with the speaker impedance characteristic shown in the graph will result in EXACTLY what you have described -- weak bass and an over-emphasized upper mid-range.
If the sound continues to be unsatisfactory following additional breakin, I suspect that among tube amplifiers a much better choice for use with the XT6F would be a medium powered Audio Research model, if you can find one used at a suitable price point. ARC designs tend to have significantly lower output impedances/higher damping factors than many other tube amps, in part due to the use of moderate amounts of feedback. Also, they tend to have robust power supplies, which may also be helpful with respect to the low impedance of the speakers in the bass region.
Good luck. Regards,