Changing the Hue device DNI in Hubitat will break Hubitat's integration because it depends on the DNI being the Hue app integration's app ID, followed by a slash, followed by the Hue-Bridge-assigned device ID.
There are two solutions that could work. In my opinion, the easiest would be just not to share these devices from Hubitat to ST at all. Both platforms have have Hue Bridge integrations that will work for this purpose, so unless you depend on immediate state changes (e.g., for webCoRE piston subscriptions on the ST side), you won't gain anything from doing it this way.
If you do want to share the devices for some reason, HubConnect is an alternative to Other Hub that I know can handle these. I'm not sure if krlaframboise is still interested in maintaining Other Hub (it definitely hasn't been updated in a while), but if so this may indeed be a limitation that might be fixable. Otherwise, there are a few alternative options--hopefully something works for you!