Clipboard across profiles works fine for me nowadays, as does the 'share' option, which brings up a screen with 3 tabs across the top, personal, work & private. Selecting 'private' gives access to the appropriate apps for the selected item to be shared.
Did you have a look at the settings for private space? Swipe up the normal app drawer until you get to the private space apps, then click on the settings icon for private space. Have a play with the settings under 'cross-profile shared clipboard' and see if it gives you what you need. Of course, what you see may be different depending on your home app, etc.