I don't want to sound like Debbie Downer here, but there are a few issues with this test.
First off, you don't actually
play anything. A sustained, open note isn't enough to diagnose the problem. For instance, what if the treble EQ is designed to affect pitches
higher than an open G? What's more, we're completely missing the complex harmonics created while fretting (er, fingering) a note. A demonstration playing across the full range of the instrument would be far more helpful. Also, if it were recorded at a quality higher than 240p we'd be able to hear much more.
What's more, you appear to be playing with flatwound strings (I'm guessing D'addario Chromes?) Those are probably the worst strings to test treble controls with. They have virtually no treble to manipulate to begin with. Really, the most obvious thing you'll hear with that setup is an increased hum when you have both hands off the instrument, but that's assuming you're in a situation that would create hum to begin with.
I have an A4 SA, which is a later model with a slightly different preamp and control panel, so the comparison may not be 100% exact. However, I just replicated your test, and on mine there is an enormous difference in the top end sound between the treble slider being all the way up (full boost) and all the way down (full cut) even while the note sustains. It certainly sounds like there is something not quite right with yours.
I should say that I haven't played an A4. However, I have played many other instruments in the A series, and am very familiar with Bagg's systems from that era. And I will say that both companies voice their instruments very uniquely. Both Godin's and Bagg's designs changed DRAMATICALLY over a very short period. In general I find it's for the negative, but a broader EQ range may be one of the changes. A more dramatic treble control may be one of the things that changed. So I have to agree with Randy Molson here. It could just be the nature of the EQ points. I don't know if they'd share it, but if you contacted Bagg's and asked about the frequency (center, cut, boost) of the treble control on that particular pre-amp, the effective range might be above what's produced by your current setup. If numbers aren't your thing, or you can't get the relevant information, there's one simple test; change strings. Some steel roundwounds would provide the most obvious results, but that's kind of the nuclear option. Halfwound or groundwound strings will really open up the frequency range, and that would help you explore the impact of the treble control while not completely destroying the fretless aspect.
If you want help "opening up" the treble on your bass, I can't recommend the dudes at
Welcome to Bass Strings Online - Your Custom Bass String Shop... any higher. Explain your problem, and what kind of sound you're shooting for, and they'll set you up with exactly what you need. (We all need to turn to the experts, sometimes.)
As for the pickup, I'd leave it alone. If I recall, it's a ribbon-based design. If that were failing, there would be different signal output between strings (one or more string being drastically louder or quieter than the others,) not general frequency output. Given that all four strings seem to have the same output level, I'd say it's working just fine.
After all that, there's always the remote possibility of a bad slider/solder joint. I know you said you've had it serviced, but hey, ya never know.
Of course, one last thing to keep in mind is that this is the A series - as in Acoustic. These instruments are designed to emulate their larger, fully acoustic brethren. They're not designed to, nor will they ever be
truly able to emulate a solid jazz bass or an active Schecter. If you can't get the tone you want out of it, you may want to look into another instrument.
So, that and a nickel won't get you a cup of coffee. But that's my two cents.
