"Carriageway". Haven't heard that term previously. I learned something new today.
Yes, that does take some adjustment, and exactly as you described. I usually bring a young person with me, the first few drives, and have them sit in the passenger front seat. They will let me know, when I get on the wrong side. The key is to start off slowly and think twice.
Two big problems for me are that the cars tend to be very cramped, and the suspension is often sloppy. For prados and sequioas, I generally replace the sway bars, shocks, and some other components with more beefy versions. There isn't much that can be done about the cramped issue.