I’ll start with noting that these repairs on the HP 3478A (and many other older HP instruments) are well documented amongst the community. I mostly referenced the excellent write-up here by Tom.
I mostly followed the procedure described, I backed up the SRAM via querying the contents over GPIB, wired in a pair of AA batteries to keep the SRAM active, and replaced the lithium cell. After which, followed it up with replacing the old RIFA caps, which are infamous, and as expected, had cracked in my instrument.