Accurately Recreating Sierra and Walden from Instagram in Lightroom Classic or Photoshop

Question

I'm trying to accurately recreate the Sierra and Walden filters from Instagram in Lightroom Classic or Photoshop. I've tried manually doing this before but have never quite got them just right. So I thought I'd take a more precise approach - I've taken a colour wheel image and applied both filters to them so I could see what it's doing to each individual colour:

^{(Click for full size.)}
Original:

Sierra:

Walden:

Both filters also add a vignette to the image as well as seemingly highlighting the centres (I chose the above colour image so it wouldn't be altered by the vignette so I could get an accurate sense of the colours):

Original:

Sierra With Vignette:

Walden Vignette:

Now I'm not sure what step is next to translate this information into Lightroom Classic or Photoshop. I'd really appreciate anyones help in figuring out this as I've been trying on and off for over a week now! Thanks.

Answer 1

After comments - & some cajoling from "management" to put my money where my mouth is (just kidding;) I had a deeper look at this.
Bear in mind, I'm fumbling through this as I really don't ever play with LUTs, nor 'portable styles'.

Yes, you can save a LUT in various forms from any set of adjustment layers, however, the result may not be quite what you thought. Playing with an image from another question, I generated a red-green shift, then vignetted the mask, so the centre stayed untouched.
This was based on work done for Creating a LUT in Photoshop with a Vignette & using an image from Why does flash make a brass subject look grey? that I just happened to have open.
_{These are all just screenshots, quality unimportant. Click for slightly larger}

I saved the result as a LUT, in all 4 available file-types (not having any clue what they all do)
I then re-imported each to see what happens. I got variations on a theme of 'wtf'.
Not what we're looking for. Re-adding a vignette to this isn't going to help.

So, after poking around a bit, I decided to save my one adjustment layer, in PSD format.

Much better, though still a bit awkward. I can now re-import my hue-shift/vignette layer & then drag it to a new image.

So, I managed it, but not particularly elegantly. I'm open to better ideas ;)

Having fought with this for an hour or two, in retrospect it's really the kind of task I wouldn't do in Photoshop. I'd give it to one of the 'modern' editors like Luminar or Affinity Photo, with their 'instant look' presets - in comparison, it seems what they're designed for. Photoshop isn't.