The most common way to lose something in Italy is not to choose wrongly. It is to choose correctly, three weeks too late.
Italy's headline sights moved to timed entry years ago. That change is invisible while you are planning, because nothing tells you that a day you have not booked is a day you have already lost. People arrive in Rome with a list and discover the list closed while they were still deciding.
The moment to book is the moment your dates become certain — not the moment you work out how to fill each day. Booking a timed entry does not commit you to an itinerary. Not booking it commits you to not going.
Leonardo's Cenacolo is the hardest ticket in Italy. Visits are in small timed groups of a few minutes each, so the daily capacity is tiny by construction and no amount of planning creates more of it. It needs to be booked months ahead, and for many dates it is simply gone. If seeing it matters to you, book it first and build the trip around it — it is the one sight that should dictate your dates rather than fit into them.
Official tickets are released on a rolling window ahead of each date rather than all at once, and the special formats — the underground levels, the arena floor, the evening visits — are the ones that disappear within minutes of release. The release window has changed more than once, so check the official site of the Parco archeologico del Colosseo (parcocolosseo.it) for the current one rather than a blog, including this one.
Both are timed entry, and in high season popular slots go well in advance. The Accademia is the smaller of the two and the one people most often assume they can walk into. Tickets from the official channel (uffizi.it) and from authorised resellers can show different availability for the same date, so a "sold out" on one site is worth a second check elsewhere.
Entry is in fixed two-hour slots with a hard cap on numbers. There is no walk-up option to fall back on. It is the sight most often described as an unexpected highlight by people who booked it, and simply missed by people who did not.