We traveled this year Feb 26 - Mar 14, starting in Paris and descending via rail to Lucerne, Florence, then Salerno.
Paris was damn cold, no question. Even with an ultralight down jacket, hat & gloves, with the wind off the Seine it felt chillier than the Chicago winter we had just left. Mostly 30's & 40's. Then in Lucerne, even though we were higher in altitude and I don't think the temps even hit 40, during the day it felt almost spring-like with a warming sun. And to do as the Romans (or Lucern-ites) do, al fresco cafes were doing a booming business even in these temps. It was wonderful.
Arrived Florence on March 4, with rain and wind, but temps a little more moderate. When the sun was out in the afternoon, we could open our apartment bay windows to the piazza and let the fresh air in. Low 50's as a high during the day, down to near 40 at night. Finally, in Salerno, Pompei and the Amalfi Coast, starting on March 9, it finally reached 60 degrees on a couple days & no doubt felt like spring. At night it was raw-feeling and I did not abandon the down jacket, but it certainly was tolerable.
We traveled at this time because my work allowed it, but if I had to pick the 'perfect' time to travel to Italy in the future, factoring in potential weather & avoidance of tourists/crowds, I'd probably pick late March/early April. I had checked it out in advance and as long as Easter was not in the mix, international flights around April 1 were identical to what we paid to fly a month earlier.
All in all, even given the semi-inclement weather at times, I have become an ardent proponent of off-season travel. I cannot tell you how we enjoyed not having to wait in lines at the Louvre, Florence museums & restaurants, or the Pompei ruins. And I can't think that approximately 2-3 weeks later would make much difference in that regard, except you'd get a little more warmth. A caveat, however. Weekends are still crowded at most all attractions--Monday through Friday are blissful, though.
Congrats on your retirement, enjoy your planning!