System.util.retarget fails to transfer user credentials to project with same Identity Provider and User Source when login auth strategy is set to Identity Provider

Hi all,
We have two projects on the same Gateway server (v8.1.42), using the same User Source and Identity Provider.

The User Source is Active Directory (only) type and also backs the Identity Provider, which is Ignition type.

When we trigger a retarget to either project it always brings us to the login screen of the new project despite these settings being in common.

If we switch the Login Authentication Strategy for both projects to "Classic" the retarget IS seamless. But this effectively disabled badge login, which we require.

Is there any way to have our cake and eat it too with regards to seamless retargets and the Ignition IDP auth strategy?

No. IdPs don't work the same way (in that, they're on balance more secure) than our "classic" auth providers.