Low tuning/Xtender/String and nut question.

[Achtane]

Hey TB, I'm currently refinishing my Jaguar Bass (it's 34" scale for reference) and when it's done, I would like to ultimately have a Hipshot Xtender on the E key. I want to be able to tune it to low A if at all possible, or failing that, low B.

If it matters, I'm probably going to install a Hipshot A-style bridge (Fender mount) just to give it a little more weight to combat the neck dive. What I'm wondering is:

-Is it even possible to have a string tuned to low A that will also switch back up and function as E? Would that mess with the neck in E? Using roundwounds, what gauge string would you even use? I'm not expecting a ton of clarity from such low notes on a 4-string, but whatever would be best.
-I'm going to need a new nut for this, right? Or at least have the E string slot widened?

Thanks in advance. I've searched the forums about low tunings and the keys, but this is kind of a specific situation.

[mech]

Even using a .110, drop D starts sounding a little floppy to me. I don't think it would be usable at B or A.

Something to consider is that when the neck relief is set for E tuning and the string is detuned to A or B, the neck is going to back bow due to the string tension being less. If your action is reasonably low you could have a lot of fret buzz.

My understanding is that the D-tuners are designed to go from E to D and maybe C. Depending on the spacing and style of your tuners you may not be able to adjust it to B or A even if everything above worked out.
mech

[testing1two]

I've gotten as low as C with mine. The problem is that the string is so floppy that the note lacks definition. Even if you tuned your open E to D and then used the extender to drop it to B or A, it would feel (and sound) like a wet noodle.

I would suggest something a bit more radical like stringing your bass B E A D and using an extender to drop from B to A.

[mech]

^^^^^ If you don't need the G.