I want to use my Apple 27" display as a second monitor with new Mac Mini

Here's my situation - I have a mid-2010 iMac and just got a new Mac Mini. I also have an Apple 27" display (with mini displayport connector) that was connected to the iMac as a second display.

I have a mini displayport to USB C adapter that I can use to connect the 27" display to the Mac Mini. Works fine.

I also have a cable (mini displayport to USB C) that I can use to connect my iMac and use it as a monitor in Target Display Mode. Works fine.

BUT if I plug in the 27" display as the primary monitor, then plug in the iMac and try to go into Target Display Mode, it does not work.

After researching, it seems the Mac Mini cannot connect two monitors both via USB C, so this seems to be the reason I cannot connect with this setup.

I've searched for a male HDMI (to insert into the HDMI port on the Mac Mini) to female mini displayport (to connect from the monitor) adapter, but every one I find says it does not support video output from HDMI port to an external display.

Any ideas how I can connect both of these monitors to my Mac Mini?

Thanks.