Fellas - I am at my wit's end...
I have seen a ton of posts and videos - all seem to be for the SDV6 on a Disco/LR3 or 4.
They show that you can wiggle the Oil cooler out of the V behind the intake pipes.

I don't think it can be done on the 3.0L TdV6(single turbo) L405...
I have probably 5-6 hours in it, my mechanic son has a couple of hours in it.. Losing my mind!
My Oil Cooler looks different than the ones in the videos.
I think this cooler is 'deeper' than the ones shown and cannot be removed.
Even if I cut off the mounting hole for the oil separator - I don't see it coming out.

Click image to enlarge

From the workshop manual .. would suggest you remove one of the rocker covers . . . . ( oh and you definitely have undone all 6 bolts ? )

REMOVAL
NOTES:
This procedure contains some variation in the illustrations
depending on the vehicle specification, but the essential
information is always correct.
This procedure contains illustration showing certain components
removed to provide extra clarity.
1.
Drain the cooling system.
Refer to: Cooling System Partial Draining and Vacuum Filling (303-03A Engine Cooling - TDV6 3.0L Diesel - Gen 2/TDV6 3.0L Diesel,
General Procedures).
2.
Disconnect the startup battery ground cable.
Refer to: Specifications (414-01 Battery, Mounting and Cables,
Specifications).
3.
Remove the right valve cover.
Refer to: Right Valve Cover (303-01A Engine - TDV6 3.0L Diesel -
Gen 2/TDV6 3.0L Diesel, Removal and Installation).
4.
Remove the oil filter.
Refer to: Oil Filter Element (303-01A Engine - TDV6 3.0L Diesel -
Gen 2/TDV6 3.0L Diesel, Removal and Installation).
5.
Remove the glow plugs.
Refer to: Glow Plugs (303-07C Glow Plug System - TDV6 3.0L
Diesel, Removal and Installation).
6.
!
Disconnect the vacuum tubes.7.
!
Remove the vacuum reservoir.
8.
CAUTION:
Be prepared to collect escaping coolant.
!
Disconnect the coolant hoses.9.
CAUTION:
Be prepared to collect escaping coolant.
NOTE:
Remove and discard the seals.
!
Remove the engine coolant outlet.
10.
NOTE:
Remove and discard the seals.!
Remove the oil cooler. V8 or else ...

yeah... I have just seen so much about the fiddley method...

Removing the valve cover gets into removing injectors, and I think you have to remove or loosen the bolts for the timing cover... maybe not...

But the right valve cover instructions are 23 pages long...
 2006 L322 HSE LUX 4.4NA Jag V8 Buckingham Blue/Ivory - 'Col Reb'
Rolled Yahtzee Aug 2023 222,222Miles
2016 L405 HSE TD6. Santorini Black over Almond. - 'Donna the Diesel'
Only L405 IN THE KNOWN UNIVERSE with an L494 Shift Lever Fitted!
97K at purchase Sept of 2023