I discovered I could count and sing at the same time by visualising the number in my head, instead of using my inner monologue. But it requires more focus to maintain.
Funny timing for this comment, just last week I was running slowly on the treadmill and was counting my steps due to curiosity about steps vs time, and decided to count using images. It definitely takes more effort but I think it's because I hadn't tried it before.
I would hold the tens digit image static and repaint the ones digit until it rolled to the next tens digit, which meant very limited effort was required to retain the tens digit image and most effort was transitioning the ones digit.
The ones digit would not just instantly flash in place, it took a small amount of time and some noticeable deliberate effort for the process to complete, and then it was just in maintenance mode until the next transition.