Another way to see the Basilica lighted, that might work with your time frame in Venice is to attend on of the Sunday masses (if that would interest you). We did that in early October, and it worked out great time wise, then we immediately went upstairs to the museum (and out on the balcony overlooking the square) afterwards. Before and then immediately after mass we walked around the Basilica to view features up close. Mass had a good crowd, but there were still a few seats that continued to be filled during the service.
On the next day (a Monday morning) we arrived at Doge's Palace and had a very short wait, maybe 15 minutes (without advance tickets). My husband absolutely LOVED the displays in Doge's Palace.
I was surprised that the main square was not more packed with people. The only place we found crowds somewhat unpleasant was along the main waterfront. Our hotel, Hotel Le Isole, was beautifully situated just a few minutes away from the main square, yet on a quiet small canal......best of both worlds. Our bathroom was very small, but we enjoyed a room with a small balcony overlooking the small canal, and a full window overlooking the other approach on the canal. Just a few minutes to great restaurants, etc.
But, that was early October, not late March.
We did not purchase advance tickets to sights, as we did not know how jet-lagged we would be. I'm glad we remained flexible.
We LOVED the vaparetto cruise of the Grand Canal (as recommended in Rick Steves' guidebook), and we took the advice to just wait for a vaparetto with seats in front of the wheelhouse, which offered incredible views. The front desk person at our hotel recommended a route for us to take that allowed us to enjoy a big loop, and we otherwise would not have known to take that particular route on the varparetto. We purchased tickets at the manned ticket office at the dock.
If we had more time (we only had our arrival day and then a 2/3 of a day before we had to board the SeaCloud), we would have climbed the bell tower (but there was quite a wait for it when we exited Doge's Palace).
When you arrive in Venice, we recommend taking the water taxi from the airport (we booked a shared water taxi on the spot to save a few $s). My husband considers the journey into Venice on the water taxi one of the highlights of the trip!