Well try it before you go Chris; save disappointment!
Have you tried it on the K5ii since the issue?

If it is definitely fine on one body but not the other it does point to a camera problem. Definitely worth doing some further tests to make sure.

The EXIF suggests the exposure is consistent between the shots so could it be the lens aperture isn't closing down. First thing therefore is to try a different lens and see if the issue goes away. Also check the lens you've used for sluggish diaphram blade closure, it is an issue that can affect some older lenses (guess it could with new ones too) and is a common cause of unexplained over exposure.

I can't recommend any specific lenses as I have no idea of your style of photography. I'd have thought you could get something really worthwhile for the price of a K-S2 or K-70 body though. If you're not getting good images from a K-S1 then it might be down to your technique or processing of raw files (if you use those) and if not, the settings for in camera jpegs which are not necessarily optimum by default.
If funds are no object why not look for a K-3 or K-3ii (perhaps used) which are higher end and more versatile models. I don't believe you'll see much, if any, gain going from a K-S1 to a K-S2 and not a lot to a K-70.
https://www.dpreview.com/products/compare/side-by-side?products=pentax_ks1&produ...

You'll note the specs of all three are not that different to each other.

Now compare against the K-3s:
https://www.dpreview.com/products/compare/side-by-side?products=pentax_ks1&produ...

Either really would make a difference.

Exactly. I often take my K-S1 out rather than the K-1 as it is one of the lightest DSLRs out there and lighter than some mirrorless offerings. I have to ask the OP, what do the K-S2 and K-70 offer for the task that can't be achieved with a K-S1 ? I really can't believe changing would make any significant difference to the results you get from the KS-1.
If spare photo funds are available, maybe look to spend them on faster or useful focal length lens. While the 18-55 is not bad, there are better alternatives. A faster lens would allow more available light indoor shots without the need for flash. A wider lens might be useful for getting group shots in confined spaces. A longer focal length lens to get more candid photos from a distance.
I'd certainly think it through again.
By the way, welcome to the forum!

I'd find it a nuisance having to rotate the monitor to view a portrait image!

PU reduces images to 1,000 pixels on the long side so for uploading that's not a bad compromise. Uploading large files to web sites slows everything down as the server has to resize them on the fly for you.

You can set the the camera to give you a DOF preview. Simpler than carrying a computer to work it out in the field.

With automatic focus there really isn't the need for pre-setting the lens at the hyper-focal distance any more. If it's an old manual focus lens and it has the DOF scale on it then it's still there to use.

I had a feeling it wasn't 100% hence not taking up the sale from Norway. It might be worth getting it professionally restored given the scarcity value (if the price to buy is right to allow for that.)

Full frame Ricoh GR ?

This lens, or at least one with the same serial number, is presently for sale on eBay.
I was contemplating it but wondering why no one seems to want to own it!

What issue?