Best way to contact pre and post-tour hotels for extra days' stay

I always email.

I've just used the hotel website to make a reservation, and then under "comment" or "special request" noted that I'll be part of the tour starting or finishing on X date, and requesting to stay in the same room if possible. Sometimes I've had to change rooms, sometimes not. I've found they are glad to accommodate me whenever possible.

We used e-mail. For two tours, we arrived early and neither time had to change the room.

Another vote for email. Not all rooms in these hotels are equal. Sometimes you may get one of the nicer ones and sometimes one of the more average ones. (Example view room vs non view room).
I will pay for a slightly nicer room pretour on the assumption that I will get to stay in that room for the tour days. So far, this strategy has worked but it is not guaranteed :)

I’ve always booked through the hotel’s booking engine and added a note that I was with an RS tour starting on such and such day. There was one time that the hotel was showing booked on their website but booking.com showed availability so I emailed. They seemed shocked their website showed full and were glad I contacted them. They booked me in.

I do the same with the Road Scholar tours I go on as well.

Email. Tell them you're on a RS tour staying at their hotel. We've never had a problem.

I emailed both hotels yesterday, mentioning in each case that we were part of a RS tour. Our tour isn't until late Sept and I'm not sure if they're booking that far in advance. Hopefully, I'll hear from both hotels one way or the other.

Thank you all for your input. I heard back from the hotel in Venice (the starting point of our My Way Italy tour). Unfortunately, they had no standard rooms available because they have another group staying the days preceding and following the night we needed to reserve. The only rooms they had available were quite expensive (540 euros and up) and outside our price range. We were, however, able to reserve a room at another hotel.