If you google the terminal maps, there are monorails that move you from terminal to terminal but be sure to wander the terminal a bit (butterfly garden at T3 and the pool at T1 might be back in action). We usually squeeze in a massage before our next flight as well... God I love Changi!
I prefer the SilverKris lounge at T3 than T2 but as you have access to the TPR, that's a moot point.
What Transit hotel terminal are you booked at?