My iCloud storage is nearly full and I don't want to purchase more. Most of the space is used for Messages. I want to KEEP the message strings (text and pictures) on my iPhone but delete them from iCloud. How do I do that?

You can turn off messages in iCloud. Learn more: https://support.apple.com/en-us/HT208532

My question exactly. It isn't possible. Apple wants you to be totally reliant on icloud. I found this out yesterday, when i lost all my notes. I have since restored my iphone from previous backup, and with cellular data and wifi off, backed up phone to a new program called iMazing. It works like icloud, but keeps it local on my computer. So then when i reconnected my wifi and data, it DID wipe out the notes from my iphone (as all notes were deleted from icloud) but at least I had them backed up locally. I am just going to use my exchange notes (from sticky notes) because Apple didn't delete those...And then I'll gradually merge the backed up notes I have on the new program iMazing.

NO! don't do that, unless you are prepared to delete all that data permanently from your devices.