I would stick to your original plan as fitting in the battery box would render it to water ingress when wading and when running through melting snow unless your battery box is water tight (no battery anchor rods passing through the floor or unused bolt holes and gaps )
as the indicators work ok the ignition fed side of the hazard switch is working .where the brown fed from as this should have a battery feed for the hazard switch to work when pulled out,try taking a fused piece of cable from a known battery feed to the brown on the flasher relay and try...
so you have had a dent and paint job where about on the vehicles would narrow the problems maybe a disturbed connector unattached earth damaged or trapped harness a fuse blown or dislodged
that the problem most of my images are around 3Mb and I'm unable to post them .the one's I post are re-sized and then further resized by the site in some cases view them in windows paint (as they are created in paint in PNG format as the colors don't bleed)
The firing order is the same for the 3.5 and 3.9 (changes when fitted in the Range Rover )your set up is one position out from the reference point but the firing order is still 1,8,4,3,6,5,7,2 so is correct but your marking are out