Post more pictures hard to see what I'm looking at even with your writing

I have no idea what you are trying to do and IMO if you can't mount them inside wou will need to do an outside mount and we need pics of the space to undestand the issue.

You usually need a nice deep recess for interior mount, unless you don't mind the shade protruding past the window trim. It depends on the type of shade, what kind of light control you want, and your window configuration. It doesn't look like you have enough flat area for an inside mount. Even an outside mount will be challenging with your window trim. You may need to mount it on the drywall above the trim. But more photos would help.

Or you could get a window company to come to your house and give you some advice.

Chances are what you are calling "shim/filler" in brown is what is known as an extension jamb. Possibly you can install the blinds into that, depending how thick, what's behind and how well attached it is. Most likely better to do an outside mount, which will also be tricky die to the window casing profile. I did miniblinds at one of my houses and they were mounted to the flat part of the casing (outer edge).

Hi, edited to include another photo.

I'd be fine with some sort of cellular shade and wouldn't hate if it came past the window a bit. I just dislike the idea of having something cover up the molding and wanted to see if there were any way to sneak a low profile cellular shade (or something else) option in there with just a small space to do it.

any thoughts?

drdavidge, what did you end up doing? I’m facing the same situation.