I decided to set aside a small budget (low 3-digit) to get data out from a ST2000DM001.

Problem: At boot, the computer takes a very long time for detection phase (AHCI) and does not detect the drive. In IDE mode, time spent on (not-)detecting the HDD is shorter but still many times longer than it should be.

The spinup and initial head activity sounds alright to me, but what do I know about HDDs. (I'll get the recording if needed, setting up the audio equipment takes a bit)

I'm going to start with a PCB swap. My intention is to find a drive with the same PCB, firmware and first 3 letters of the S/N.
The question is the ROM swap that I've been hearing about. Two things 1) I'm worried that I or an unprofessional repairman would botch the job and destroy the chip and hence all possibility of data recovery, and 2) what does the ROM chip contain? This repairer says "Every BIOS IC of this type board is unique to it's original Hard Drive, BIOS IC swapping is a must !!!" but this person is asking for the ROM files. Does the ROM chip contain something that is unique to each individual HDD unit, or is it just something common to the production batch/configuration/firmware version/PCB?

The "repairer" is right about the ROM.

What makes you think your drive has a PCB issue? If your sound description is accurate, then PCB issue is very unlikely.

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Hard Disk Drive (HDD), Solid State Drive (SSD, SATA, NVMe, etc), USB Flash Drive and RAID Data Recovery Specialist in Massachusetts

I agree that the problem is NOT the PCB but somewhere else.

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Death is nothing, but to live defeated and inglorious is to die daily.
Data Recovery Cape Town

you asked & answered ur self

good luck

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Kuwait Data Recovery - UNIX GTC
The only reason for time is so that everything doesn't happen at once. By: Albert Einstein

Simple : choose carefully.

In case everything or something goes wrong, there's always a solution - just call. (note : it's not cheap).