I work in the printing industry & while I appreciate the general consensus is to use sRGB for publishing to the web due to it not using the dynamic range contained within aRGB & also supposedly rendering the image better as it doesn't have to convert the aRGB to sRGB & therefore might get it wrong thus causing your photo to look odd, maybe.
I say maybe because I have always used aRGB for posting my images & have done some tests uploading the same image, one of each & looking at the pair side by side & am unable to see any difference.
And at my place of work we always ask for aRGB, when on the rare occasion we are sent sRGB we contact the client to see if they have an original in aRGB.
When exporting in sRGB you throw away data which is the dynamic range, so why do it when there is next to no difference when posting to the web.
Just process in aRGB & you'll keep all the data & by default the best image you can process.
ProPhoto in LR has quite possibly a better dynamic range than aRGB but until the industry changes which will take 20 years at least the best you can achieve is to not use PS & only LR & print / export from there.
Not much use if you need some serious manipulation.
I haven't upgraded my PS for some time & am still using PS 5.5 extended, does the new version 6.? have the ProPhoto available to use directly from within PS?
Each time you switch between one colour space, basically a ICC profile, you will alter the data that compiles the actual image & thus give rise to banding & fringing.
My first suggestion would be to change your PS setting to use aRGB & when saving not to convert to sRGB even if web publishing.
Unless of course someone specifically request sRGB but of course always keep the aRGB original file along with an untouched raw file.
And that leads me to ask, do you photograph in RAW?
Photographing only in jpeg will certainly cause banding/fringing due to the processing that has already occurred within the camera & then within LR & or PS.
Each new edit causes damage to the file with manipulation of the pixels, even saving a photo that in the camera is say 240ppi & then we after editing save the image at 300ppi.
This causes interference & issues with the quality of a photos appearance.
I only ever up scale the ppi of any photo if I know I have finished editing & it is going to its final destination, print or other media.
However, I always have the completely untouched RAW file I can go back to no matter how many times I have used & edited a file, I always only ever edit from a copy of the RAW file.
I won't even risk thinking I will remember to 'save as' just in case I forget as for every stroke of the edit mouse/pen you alter the data, even if you 'edit undo' the mere action of doing something & then undoing it causes the original data to alter.
One quick test you might be able to undertake if you have access to a printer, print out an unedited original photo direct from the camera & compare to see if the banding is there even if it is on the cameras screen
This test isn't to check for colour, clarity, tone, exposure but simply if the banding is there.
If it is then it is likely to be camera settings & not any editing software.