My Amiga 2000...

[Tenacious]

What are you ultimately going to do with your A2000?  If you are going to standardize it (find an inexpensive 2091, SCSI HD, SCSI CDwriter, SCSI ZIP drive, newer OS, etc), simply compress and move everything to the larger HD.  You can then find the best Amiga to PC transferr method at your leisure.  

On newer larger HDs, make lots of partitions.  Make some the size of CDs (700MB) for things like: Applications, MyFiles, Archives, CDimage (a place to organize data before writing CDs).  Make a handful of 100MB partitions for: SYS:, a backup of SYS:, an alternate SYS:, Internet Apps: (iBrowse and mail programs generate tons of small files).  You could also make a 32 MB MSdos partition.

If you like to control how install scripts behave, don't name any partition WORK:.

[Tenacious]

What is the purpose of having those small partitions, as opposed to just leaving it as one big filesystem? I gave up partitioning my drives in the PC world over 10 years ago as I was sick of having to shuffle files around and resize partitions...

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Amiga OS can benefit from logical partitions.  It might be one the best organized (and most user accessible) OSes available.

Multiple small partitions allow flexibility in running and trying different OS configurations and different versions.  Unless you are well versed in AmigaOS, backing your boot partition (to another partition or drive) can have advantages.

Also, separating static partitions (those that are written less frequently) from Apps that are constantly writing and revising small files might greatly facilitate data recovery when the HD eventually fails.

[Tenacious]

Maybe your serial cable is a straight-thru type.  IIRC, the transmit pin at one end is supposed to be connected to the receive pin at the other.  This is actually true of both ends.

Just a thought, easily checked with a continuity tester or meter.