I'm not sure if this is 'homebrew' exactly, but close enough, maybe..

I was looking around via Google, but found allusions to rather than direct
sources, of an internal modification to allow the unused middle connector of
the antenna socket to allow an external AM antenna. I've not found the
article itself, or any pointer saying exactly where it is either. All I have
is a name, Laurie Mann, in Australia.

I'd already tried coupling a long wire directly to the AM input after
unsoldering the wire on tne non-grounded end of the winding on the ferrite
rod, with no meaningful improvement (as expected, it worked, but was too
noisy to be helpful in any way). While a car radio will take any bit of wire
as an antenna the PL-390's AM isn't meant to work that way. I'd already tried
doing that with the winding still soldered in place too, with no convincing
result.

If anyone's worked on this particular radio to improve AM, especially by neat
internal work like a rewound ferrite rod (because apparently the Si4734 DSP
Radio IC will take a wide range of inductance), I'm interested to hear about
it. Also, any other useful modifications...

Last but not least, I'm not so sure that its AM performance on long wave is
as bad as is often claimed. Maybe it's just not as excellent as much of the
rest of the radio, but as an example of LW reception I have this:
On Ashton Court, just over the Somerset border south west of Bristol, 48
miles away from Southampton, I picked up an NDB transmission 'EAS'. I did not
know it existed beforehand, but heard it well enough after several minutes to
note its code unambiguously so I could look it up after returning home. That
NDB has a nominal range of only 15 nautical miles, and what is worse, it has
to compete on 391.5KHz with Cardiff on 388.5 KHz. Cardiff is very strong, and
very close. Worse yet, its bearing is W, and Southampton's is ESE, so it's
not like I can use the orientation of the radio to help a lot. Despite
this, using the 1KHz filter which DID help a lot, I could select the
ghostlike distant EAS signal while completely excluding CDF. On any other
filter, CDF blasts all over it, and the AR-3000 at home was utterly helpless
with its 8 metre high vertical whip. Sensitive, sure, but about as selective
as the aim of a blunderbuss.

In short, I think the Tecsun PL-390's LW AM performance is a LOT better than
it is credited for generally, but all the same I'd like to have a crack at
seeing if I can hear an NDB from london to Bristol. I know, little things
please little minds. But it's a very fun way to learn so I want to have at
it, and I'm interested in anything anyone has to say if they have worked on
modifying this specific radio in any way.