Recovering a LUKS partition

I have a drive with 2 partitions

• 1st is plain ext4


• 2nd is encrypted LUKS.

The partition table has been overwritten. I've found the beginning of the second partition, which I need to recover, thusly:

# hexdump -s 400000m -C /dev/sdc | grep LUKS
61d3dec850 79 c8 81 6d e5 4c 55 4b 53 40 49 aa 29 df de d7 |y..m.LUKS@I.)...|

Also:

# losetup -o 0x61d3dec850 -r -f /dev/sdc
# losetup -a
/dev/loop0: [0005]:477209 (/dev/sdc), offset 420166420560

So far, this problem pops up:

# cryptsetup luksOpen /dev/loop0 luksrecover
Device /dev/loop0 is not a valid LUKS device.

Is it wrong offset? Should I seek for the magic number 0xEF53 identifying ext4 as adviced here ?

It's a 1TB drive so please, I need an advice that does not force a scan of the entire drive all over again (e.g. testdisk which seems have no option to start at a specified offset to save time on scanning).

P.S. This question seems to be closely related but does not match.