BaySt...you went from a $2-3K tube integrated amp to a $15K tube integrated amp! May I offer up a few comments/suggestions/questions?
1) Have you ever owned a tube amp before or have you listened to one extensively? If this is your first foray into tubes, I would not start out with a $15K tube amp as you may find out that the tube sound is not for you and the hit on a $15K amp on resale vs. the hit on a $3-5K amp will hurt a lot more.
2) I think buying the integrated sight unseen and unheard is a big risk unless you are willing to take a big hit on resale if you decide that the amp is not for you, so I would start your list of options by what is available to you to hear locally (preferably in your own system if local dealers are willing to let you demo at home with your speakers).
3) I think you can get very good tube integrated amps in the $4-6K region which should be just the right fit with your speakers. One good place to start is the Prima Luna Dialogue HP integrated which can accommodate 6550, KT-88, KT-120 and KT-150 output tubes, and it has an autobias function which means you don't have to worry about that PIA issue but again if you cannot listen to one locally, you may want to see if an out of state dealer would allow you to demo at home and if it's not to your liking will charge you a modest fee plus freight charges.
4) Do you have a good sense of the SQ attributes you are looking for? Tube circuit designs and different output tubes can have very varying and distinct sonic flavors, so a little research up front first to define what type of sound you are seeking and secondly narrowing the list down to those amps that will deliver on those attributes will be hugely helpful. Again the PL Dialogue HP comes up here because its flexibility in accommodating 4 output tube types and playing them in Triode vs. Ultralinear modes allows you to contour the sound somewhat to better match what you are looking for and what best works with your speakers (please note I have no affiliation with PL and have never heard it or owned it but I am using it as an example of a well-reviewed, properly designed tube integrated amp that has a lot of flexibility and that does not cost an arm and a leg).
5) Your Diapason speakers are rated at 91dB sensitivity @ 1w/1m and has a nominal impedance of 6 ohms, which suggests on the surface that they should work fine with a tube amp but there is a drop in the impedance curve to 3.4 ohms at 200Hz (upper range of midbass frequencies) so you would still want to have a capable amp with sufficient current delivery via the 4ohm taps to make sure there is not a hesitancy or a diminution at 200Hz where a lot of what we hear as bass information is really midbass info. To see what instruments lie in this region, refer to the chart below:
6) One final option to consider is a hybrid integrated amp, with tubes placed in the preamp stage or the input stages of the power amp and a SS output stage, which should give you some tube flavoring without the hassles of dealing with changing out output tubes every few thousand hours and biasing them etc...One option that comes to mind that I think is an excellent hybrid integrated amp that is also from Italy (like your Diapasons) and that is visually very striking (some people love it and others not so much) is the Pathos Logos (now in mk II version). I have heard the Mk I version which a friend used to own with his Focal speakers and it was a match made in heaven. Here's a pic of the Pathos Logos in case you are interested (but remember there are many such designs including an option that has been talked about here a lot, the Musical Fidelity Nuvista 800 integrates amp):
Pathos Logos:
Musical Fidelity Nuvista 800:
I am not trying to dissuade you in any way from going after an integrated tube amp (I run tubes in my system) however I always err on the side of up front preparation and research so you can make the best decision the first time around and I find the best research, beyond reading reviews and asking questions on fora like AA and others which should help in winnowing down the list of demo options, is to listen to as many candidates as possible (a few times if possible) and arriving at your own conclusion as to what will best match your sonic priorities and best fit your speakers and rest of the system.
Good luck.