How can I run Mojave on an iMac that won’t run Mojave?

Last week a relative gave me his old iMac 27” 2011 [HDD]. I Planned to run it off a bootable external SSD with Mojave 10.14.6 installed — I wasn’t aware of the hardware limitations i.e. the iMac’s hardware only supports MacOS up to High Sierra.

How could I run Mojave on this iMac?

Responders may suggest 1) patch with dosdude's patcher (not compatible with this model iMac) or 2) use High Sierra. My problem with the 2nd suggestion is that I'm already set on Mojave with software licenses (with machine install limits/hardware locks etc.) and all sorts of custom software patching setup for audio production that will be a nightmare to replicate (obviously I can't use a Mojave Time Machine BU to go backwards).

Any ideas welcome.

You could try http://dosdude1.com/mojave/, although I don't know if that would work in your configuration.