I go with the “however you get it done” approach
If you rotate your thumb to the bottom of the neck, it will help with your reach, when needed.
I tried that too but it was really uncomfortable
So, here is an issue that I’m facing, and maybe you fine folk may help.
At present I’m on lesson 73 of B2B plus I’m doing some additional exercises and noodling, as well as trying to learn some simple songs. I managed to do HotRS all the way through. I usually learn bass lines like @JoshFossgreen suggests in bite-sized chunks (crunch, crunch!) and I glue the chunks together (gloop, gloop!). This usually goes quite well. However, when I try to play through a song, or at least a longer stretch, after one or two reps I miss bars, or misplace bars, or get stuck on a chug where no chug should be (you know, like knowing how to spell banana, but not knowing when to stop and ending up spelling bananananananana).
Interestingly, I can chug or gallop to a 4/4 beat or a train shuffle up to 120bpm for 10 minutes without missing too many beats, so it’s not a question of endurance.
Would you guys know some exercises to develop a good memory for keeping up more complex phrasing over the length of a song?
Oh man I have this issue badly myself as well. Sadly the only answer I have is a lot of repetition of the song. The other option is sheet music or tab to follow along but I have even done this while reading on other instruments 
What I do is isolate and practice transitions, both in and out.
This is very normal behavior, your body wants to keep doing the pattern its doing.
I isolate just before the transition a bar or two, create a loop, slow it down, and burn it into my skull. Focus on where your hands are, and where they need to end up.
The other thing to do is listen for cues in the song, drums, vocals, whatever, that signal the transition is coming. They are usually there.
Once you do this a few zillion times you start to be able to handle transitions better.
That’s an awesome suggestion @John_E , I’ll definitely do the transition isolation exercises. It seems obvious, and yet I missed it. Sheesh!
BTW. How did you fare with the wallered out truss rod socket?
The stew mac wrenches are out of stock, waiting to order them and give it a whirl before I strip it out any more.
That’s because you are thinking instead of playing, learn the chords and transitions of the song and try improvising bits you are having hard time remembering…or try improvising whole song on your own couple of times. When you get into habit of doing this all pieces will start falling into it’s place.
Know the chords of the song, and just play the roots. As you get comfortable with that, add in more complexity a bit at a time. Play with the song and you’ll know when a shift is about to happen
How do you eat an elephant? One bite ata time
I struggle to memorize it when I don’t really know the song.
If I learn songs that I know really well, then its not a problem.
I just covered a Slayer song, that I know really well.
It is over 6 min long, and I learned it in about 5 takes, then played it for 2 days straight, then covered it.
If I try to do this with a song I don’t know REALLY well, then I have troubles with it.
Even with songs that I know well, but not really well, like Iron Man, I know it, but can still blow some transitions, due to length of song, and I just never committed it to my soul, and only just know it well.
I am working that cover next, so I am listening to it alot, just to really be at one with the song.
I had trouble with the speed and finger placement of Billie Jean. Definitely like a tongue twister for your fingers. Also it sounds like garbage when I play… I figured that I’m un-learning basic muting techniques as I go along, and forming bad habits. I forgot about laying my fretting fingers across the strings to mute all the others I am not using. I also forgot that I can simply lift my finger slightly to mute a string I’ve just plucked. It’s been better making a more conscious effort to do this - but all of this improper fretting and position of my wrist has lead me to an injury so that is my worst struggle 
Welcome aboard, @zeef . . . 
Billie Jean is definitely tough and I struggled with it myself . . . as time goes by and you get more practiced, things will even out. Have fun with it and don’t get discouraged!
Cheers
Joe
Welcome @zeef ! Practice slow and build up speed. You’ll get it, we’ve all been in your shoes.
Ok, wow. How did I not know this? I think I’m fretting way, way too hard? I brought my bass to a “local guy” for a set-up but I’m thinking he has no idea what he’s doing because I don’t think I could possibly fret without my thumb behind the neck.
If I posted a crappy video of my fretting hand would some of you experienced guys like @howard be able to tell if I’m messing this all up?
I’m pre-emptively ticked off because if I’ve got a bad set-up then I’ve been teaching myself bad fretting habits for a year.
Your habits are probably fine, but you may have been forced to work too hard 
It should just take a little counterpressure from your plucking arm to be able to fret notes without using your thumb on the neck.
It would probably explain why I struggle with speed when changing notes/frets on the same string. Dumb stuff like the 5->3 of the 5->3->0 on the E string for Another One Bites the Dust. Just difficult for me to get it at full tempo.
One thing to try is to measure your action height at the 12th fret, from the bottom of the E string to the top of the fret wire. Mine is about 2.25mm on one bass and 2.5mm on another, for comparison.
Edited, Fender recommends 0.015-0.2" at the 8th fret with a capo on the 1st while fretting the 17th.