Hi Mike, quite honestly, I have had that exact same issue with 2 Alembics (out of 3!) that I've owned. I'm just trying to get to 0.012" as recommended in Joey's setup guide, which is even less than the typical ~0.015" I have typically heard as "normal" relief on regular non-Alembic basses. But I could only get ~0.004" with the truss rods completely loosened - so lots of string buzz on the lower frets.
I'm not sure what to make of that... I've never had a problem getting at least "normal" 0.015" on any other non-Alembic bass I've ever owned. I know it CAN be an issue on any type of bass, but let's just say I've had this problem more with Alembics than anything else, whatever the reason.
Regardless - here's some guidance based on my experience:
- Edward is right that heavier gauge strings might help. But I'll add that string TENSION may be the most important factor. This often goes hand-in-hand with gauge, but not always - you can get medium-gauge strings are that low, medium, or higher-tension, for example. You could try strings that are known to be higher-tension, and see if that helps (if you don't mind higher-tension strings, that is). Offhand, I think that GHS Boomers are somewhat higher-tension, if you're into roundwounds. If you prefer flatwounds, my understanding is that this is even better - flatwounds tend to be higher-tension than roundwounds, although there is still a spectrum.
I personally do prefer LOW-tension strings. So I admit that this doesn't help the neck relief issue - but again, all of my other basses can do it without a problem.
- You can try heat treatment, or a "heat press".
First, just a general disclaimer - I'm not a guitar tech, so this is just based on my research. I would always recommend doing some further research on your own, of course.
This involves heating up the neck while applying a force in bend it in the direction you want - e.g. clamping the neck in the middle to bend it downwards. The heat allows either the wood, glues, and/or finish material (depends who you ask) to permanently adjust, ideally. You're basically resetting the "normal" position of the neck to add/subtract some amount of relief.
From what I have heard, the biggest risk is simply that the improvement MIGHT only be temporary, so you waste some money. i.e. After maybe a week or two, it might go back to the original position. But if it is done correctly, I have generally heard that most people have had positive results. Obviously, care should be taken to not clamp the neck so much that something breaks, but that seems relatively unlikely as long as you're being careful.
You could take it to a well-regarded guitar shop, and have them do it. I would suggest contacting them first to make sure that they have done it before, and agree that this is a good next step. There are even specialized heat press machines that some of the bigger guitar shops own; it's specifically built to do this.
For my first Alembic that had this issue, I contacted Alembic, and ended up sending it to them to do a heat treatment. So I know Alembic themselves are able to do this, or at least they were at the time. This was a long time ago, so I don't remember exactly how much it helped in actual numbers, but I seem to recall that there was some noticeable PERMANENT improvement.
For my second Alembic bass, I did as much research as I could, and then I did it myself. If you want more details, feel free to let me know via the email icon and I can send you more info. After doing it a couple of times, I was able to get the relief from 0.004" to 0.007". I stopped there, as this actually feels OK for now. I wish it was 0.012", but I can always just do another heat press(es) later - I just haven't gotten around to it.
Good luck!!
Mike D