The original wiring looks pretty much like a bodge anyway, so you may even be able to improve upon it!
With the new caps, mechanical rigidity is king--- make sure they can't "wobble around".
Only then, approach the wiring of the ground connection back to the chassis.
Make sure the connecting wires (if you are using the original ones) & the chassis connection are really clean,
(I would use a stiff brush & IPA or similar).
When you make the ground connection, use liquid resin flux & a large enough tip to heat the connection up quickly.
By the the way, I would be seriously tempted to send that diode bridge "to rectifier heaven".
It probably has, at worst, been subject to considerable overload, & at least, covered in conductive/corrosive "gunk".
PS :- looking at the second pic again, you seem to have already done a good job with the cleanup.
Maybe scrape some of the remaking brown discolouration off?