It seems as if I'm missing some technique to be able to make progress on this one - apart from guessing and seeing if that results in a contradiction later on. Can anyone share some insight?
For the next step:
Look at the bottom four rows. Three regions are entirely contained in those rows, so they contribute 6 stars. Now look at the 11-cell region on the right side. It only has three cells outside of the bottom 4 rows, and they are configured so that they can contain at most one star. This means that for the 6-cell region at left, only one of its cells in the bottom 4 rows contains a star, so R6C2 must contain a star as well.
You also have some logic to exclude stars:
from R2C6 and R3C8 with the snaky 8-cell region at top. Each of the remaining L-triominos can only have one star, so each has one.
One other thing:
Look in the right-most 5 columns. Four regions are entirely contained, so the remaining 2 stars must be in a 6-cell range: R3C6-R6C6 plus R5C7 and R6C7. The 2x2 square in the lower region then contains at most one star, which breaks things open.
You can try dividing the grid in some useful fashion. For example, if you look at the area inside the blue rectangle here:
You know the area with the blue border has to have 8 stars. Six of them come from the three rooms fully inside the blue rectangle, highlighted in pink. The rooms highlighted in yellow can have at most one star outside of the blue border. So to keep the blue area to a total of 8 stars, both of the yellow areas must have a star outside of the blue rectangle. This gets us one step further, and you can continue from there: