I started working a 3-whistle league this year as well. Even though I had learned it at camps, it still took some time to get settled in and feel comfortable. Here's what I would worry about if I were to start over again:
Call the game. It's still basketball, you're still a referee, making the calls is still job 1.
If at any point during a live ball you're uncertain about what you're supposed to be doing, the answer is always "refereeing."
Keep an eye on the lead, he's the key to your rotation.
You can worry about dead ball stuff (i.e., switching) during the dead ball.
Be aggressive. It's a lot easier to be aggressive and then learn to "leave that one alone" than it is to be timid and learn to "step up and get that one."
As the L, look for reasons to rotate. Again, it's better to be agressive and learn when not to rotate than to be timid and realize you should have rotated.
Communicate with your partners. It's much better to shout "Hey, John! You're lead now" when you've got T and C on the same side than it is to wait for John to realize on his own.
Watch your area.
Call only your lines.
Once I'd gotten comfortable with these, then I'd work on:
As T becoming the new L, worry about getting to the baseline to receive the play. Let the T and C worry about refereeing the transition.
Learn to love the C. It's the best position out there. You have the best look at most stuff happening in the paint. This is the look that makes 3-whistle so much better.
As the C, a foul against the shooter when he's rolling to the basket away from the L in the post is all yours, baby. Go get it!
Don't rotate as L until all three of you are in frontcourt.
As T or C, on a shot from your area, you need to watch the shooter all the way back to the floor. Your partner will get the GT/BI stuff.
As C when the play goes the other way, freeze a moment to see if the T needs you to stay and help.
That was the stuff I needed to learn this season. Ask me next year and I'll have a different list 😉