Thanks for all the insights. My resolution/plan is this:

I will access the landside IASS lounge.
After, and if allowed, I will clear through T2 to access the airside IASS lounge at T2. Then I will try to use the airside shuttle bus to get to T3.

I will report back later and post here the results. Hopefully, the plan works. I will also post how that shuttle bus works. Until then!