Read Full disk encrypted volume over target disk mode

My 2012 Mac Mini (High Sierra) has a full disk encrypted system disk (file vault) but will no longer boot. At power on, it shows the list of users who can unlock the volume, then shows the progress bar for booting, gets about 75% of the way along and shows a solid white screen with its CPU fan running full tilt. I backed up a fair while ago, but there are things on the disk I need to recover.

This symptoms began after a system crash which appears to have been precipitated by upgrading VMware Fusion, which may have updated some sort of kernel extension or something which has stopped it booting.

I have tried the following to get it to boot on its own:

1. Safe mode boot - just does the same thing.

2. Reset PRAM - no change (though that did get it to get to the stage of showing the users who could unlock the volume, prior to which it just went to the white screen and eventually powered itself off after, I suspect, getting too hot.)

3. Cleaned the dust from the machine - no change.

4. Tried it with only one bank of memory (tried both DIMMS) in case of memory fault - no change.

5. Extended apple hardware test - all clear.

6. Boot in internet recovery mode - just does the same thing (75% progress bar and then white screen).

7. Create MacOS install medium on an external USB drive. Same thing: doesn't even start the installer, so I can't even re-install High Sierra and try and keep my files.

I have also bought a thunderbolt cable and connected it to my laptop and booted it in target disk mode. In that scenario:

1. The laptop sees the disk but will not attempt to mount it.

2. Listing core volumes does not show the disk.

3. Disk Utility on the laptop sees the disk, but no partitions. BUT

4. Two partitions are plainly there, one of which is the vast majority of the disk. (I know this because macOS creates devices in /dev for them.)

5. Attempting to mount either just gets a volume called 'EFI', which is not the system disk.

Question is, assuming I am going to have to reformat and start again, I should very much like to recover what is on the disk first. To do that I need to be able to unlock it using target disk mode, but to unlock it the volume needs to be seen in core volumes - which it isn't, so I cannot use the command link unlock, or in Disk Utility.

Does anyone know what has gone wrong and how I can recover my data?

If it is relevant, my MacBook Pro is still on El Capitan - I am reluctant to upgrade it unless I really have to in case it goes the same way because I use it every day for work.

Any help gratefully appreciated.