Anyone with experience of 15-85 (and ideally 17-55mm, too)?

To me the crux of your issue is that you want a significantly wider range that will not require you to change lenses in the field.  The two lenses that you have indicated do cover a slightly wider range than your current 18-55, but certainly in the case of the 17-55 barely so.

As you may see from my profile I have a lot of Canon gear, including at one time a 17-55mm lens. I was frankly disappointed with the IQ and sold it. I have actually two 15-85mm lenses and like them both because of the sharpness of the images they produce and the wide range they cover, especially from the wider angle end. This lens has been described as the "secret L series lens" because of the way in which it handles a very challenging focal length range. Getting a lens with that extra 3mm on the wide end requires a lot of engineering and while the lenses have some compromises they can easily be ironed out in post processing with lightroom or Photoshop. ANY zoom is a compromise and it is unfair to compare it to say a prime lens.

I would seriously suggest you look at the Canon 18-135 IS STM lens.  It comes as a kit lens with many XXD cameras and is generally regarded as a good lens of its type.  Again it will cover a wide range, but that seems to be what what you are seeking and the two units I have owned have rendered excellent results.  The question of choice between the 15-85 and 18-135 would be where you want the extra reach?  If it is at the telephoto end, which you seem to indicate then the 18-135 IS STM is a good unit to consider and you may well pick one up second hand from someone who got it with a kit.

I was intrigued with your comment that your camera body creaked. My question would be why it should do so if you are holding the camera in the "approved manner": I.e. placing your left hand under the lens, thus carrying the weight of the lens and body, leaving your right hand to lightly manipulate the controls on the body. Consequently the grip should not be taking any significant weight except when you are porting the camera.  I still have a 650D and even with a hefty 70-200 L lens on it has never made even a whimper...