Based on the excellent advice from some folks on this forum—Sherman and RAS, in particular—I picked up a '91 Pasquini Livietta (complete with the lovely stanzas of poetry). Last week I gave it a good cleaning, descaled both hydraulic circuits, and debugged some minor things, like the vacuum breaker. The goal was simply to verify that the machine holds, heats and pumps water. (It does.) The case is a bit dinged and scratched, but it's a lovely machine under the hood.
After I verified that this was in fact a 54 mm group, I got a tamper ordered. (As RAS has noted, a 55 mm tamper is a perfect fit.) My tamper and knock box arrived from Olympia, WA yesterday. So I've had all of 24 hours to pull test shots and make a couple rounds of cappuccini:

While I'm a long way from pulling god shots with 1/2" of crema or making latte art, I have a mid-century KyM grinder roughly dialed in and am in the ballpark for extraction time. Looking forward to getting better with practice.
One of the things I'd like to do next is verify the boiler pressure. Seems like a good thing to do every 20 years, whether it needs it or not. ;^)
(That's a joke—I realize it should be done more often. It just probably wasn't a high priority for the previous owner. Apparently this machine was recovered from an abandoned storage unit.)
Quick poll for the Maximatic/Livietta owners out there:
1. What setup are y'all using for the boiler pressure test? And what's the approximate price point?
2. Also, can the same gauge be used—presumably with a different hardware configuration—to test pump pressure at the portafilter?
The flow volume on my machine seems "about right"—both with and without a puck—but I'd like to verify the pressure if I can.
One more shout out: Orphan Espresso has been an extraordinary resource. People here know this already, but it's really amazing at how much Doug and Barb rock. First of all, they have the gaskets and seals needed to overhaul these machine, as well as compatible parts (filter baskets, handles, etc.) They even contacted me when I ordered a part that they thought might have been a mistake. (It was.) Right now, I'm really just stockpiling gaskets, in case anything leaks, and hoping I can put off a complete overhaul until my schedule is more accommodating. However, I've already made extensive use of the OE videos online, and am sure I will be doing so many more times in the future.