1 x 1 1/8 nightmare

The shim you linked too goes inside the fork steer tube before you slot the quil stem into it. You would still need to get a threaded fork or clamp above the headset like an ahead stem does.

I can think of a few 1 1/8 threaded headsets but the forks aren't threaded so unless you plan to swap/modify them to make them threaded it's not going to work.

https://chrisking.com/headsets/hds_gnut
https://chrisking.com/headsets/hds_2nut
http://www.condorcycles.com/Headsets/8165-Condor-Uno-Headset/flypage.tpl.html
ect ect list goes on

I think it's going to come down to a choice of which parts you like most/least to sacrifice.

Maybe? Have seen a few of these on builds that didn't look totally "ahead".

http://store.velo-orange.com/index.php/components/stems/threadless-stems/vo-tall-stack-threadless-stem-31-8-rise.html

I considered that one and also Nitto NJ-89, but I still wouldn't be able to use the DA headset :(

Have you tried an inverse shim?

Which particular one do you have in mind?

If a Gazzetta is your dream bike I recommend a dream upgrade.

What is your dream bike?

Thank you all very much for the responses! I think if I had to sacrify one of the components, it would be the fork. Then I could get a 1" threaded fork, which means I could use the DA headset HP-7410 using shims for the headtube and also my Cinelli XA Quill Stem, but I couldn't find a 1" fork that would fit or look nice on the 60cm red frame!