Some great suggestions given already! Here are a few of mine.
DO NOT PLAY THROUGH THE PAIN!!!!
Firstly, as a player of both the bass and guitar, I can say, like others here, that the motions for picking on the two instruments are NOT the same. The response curves of the two are drastically different. While exercises from the guitar are applicable note-wise, the technique used to play them should be totally different. Using the technique for a sword when holding a battle-ax will not work and will hurt you terribly.
1) Pick physics - A lot of players seem to be suggesting that going up a couple of gauges will take away some muscular strain. While I don't doubt that these guys have had a positive experience with heavy AF picks, I take a different view. Do experiment with your gauges but be aware there's a point of diminishing returns which you should watch out for.
The point of diminishing returns - the reason I shy away from huge picks
After a certain thickness, the pick becomes a rigid structure with no flex (ex. 1mm ultex) and so is already transferring almost 100% of the force you apply to the string (100% efficiency). So if you're hitting as hard as possible, why doesn't increasing the pick gauge after this point yield any further increase in amplitude then? Because a pick/string/pickup system only has so much headroom to give. Once you've reached it's maximum possible vibration, hitting the string harder will not yield any further increase in amplitude. It may result in a broken string. It may enhance string attack, but you shouldn't try to compensate for the limits of the pick/string/pickup by hitting the bass harder, it gets you nothing but damaged hands. And your poor bass is giving you everything she's got captain! Also, I consider playing with a rigid pick over 1mm to be like playing a brass instrument with an air compressor, massive but lacking subtlety when required...
Bendy picks as force multipliers - advantages of lower gauge that I've experienced
A lighter pick does flex and as it does (in the moment before it pings through the string), the amount of force applied rises owing to the elasticity of the pick/string material. It may even rise to the same point as a thicker pick, giving you the same output anyway (only the more flexible pick is acting as a shock absorber between you and the string

). You can also gain extra dynamic from a more flexible pick by going from a nice loose grip to a slightly firmer one anyway.
I hesitantly add that the perfect pick doesn't exist. Almost yes, but perfectly suited to you? Unless you fabricate it yourself, no. So I say go for the gauge that affords you the most control of your dynamic range, that is neither too flexible nor too rigid, while giving you some comfortable shock absorption and a pick attack that is pleasing to you. There is a 'goldilocks zone' where these factors are nicely balanced. Experiment to find it!
2) Health concerns over picking by the neck or bridge? - It is obviously not my place to dispute Carol Kaye or anybody else. However, I've noticed people sometimes conflate the issues of picking safely with picking location. I only see picking by the bridge as unsafe when the pick gauge/string tension is so high that picking the string there becomes like hitting a solid object, no? Your skeletal, muscular, and nervous systems are getting severely pounded every time you impact the string. But this is an issue of body mechanics and total tolerance of mechanical stresses, not where on the string you've hit. A slightly more flexible pick will help to negate this problem, regardless of where on the string you pick.
Isn't the point of picking by the neck (other than timbre), to get some shock absorption from the increased travel of the string there? Isn't getting the absorption from the pick instead so you can play wherever you want without pain more efficient?
So pick by the nut if the song demands it! Throw picks at the bass! IMHO, where you pick is a timbral decision. If your equipment or technique prevents you from accessing the full timbral palette of your instrument, you need to adjust your equipment or technique, surely?
3) Picking technique
I say the same as most people. When it comes to refining any technique (picking included) there is only one primary question. Not 'how do I do this move?' or 'what part of my finger/pick do I use?', these are secondary and subjective questions. The primary question is this:
"How relaxed are the muscles surrounding the task?"
You do need certain muscles/groups to pick, but the body's natural reaction when doing something perceived as new/difficult, is to support the working muscles with the others not being used. This creates muscular isometry (simultaneous pushing/pulling) which is satan and the devil! You are literally wasting energy on nothing! For example, if you've fretted the string correctly and it's not buzzing, how will pressing harder help you? This isometry, will cause you so many health problems in time. Treat it as your mortal enemy.
You need to get your both of your arms completely and bonelessly limp from shoulder to finger-tip and they need to, as much as physically possible, stay that way. Concentrate constantly on releasing the tension from your muscles and developing a smooth and graceful motion around the whole instrument. Only ever use the amount of force required to do the job, never a cent more. It does take some willpower/focus but, if you can do this effectively, it's possible to remain relaxed at any tempo while hitting any subdivision. Playing the bass goes from manually challenging to a relaxed and serene experience.
Lastly, "Anchoring" makes me think of solidly grounding something, maybe too solidly? On guitar, anchoring with the R.H. ring or pinky is good practice. It isn't so on the bass. For guitars of all types, the most instinctive anchor-point I've seen is the interior surface of the forearm or crook of the elbow. If you solidly press your arm into the upper bout of the bass like this, you will get tendonitis or inflammation of some description, I've seen this too in bassists and guitarists. Muscular isometry will have the roughly similar effects. As will gripping the pick too tightly. Instead of anchoring your arm at a point, try to think of that point as a guide that your arm glides smoothly over or around.
Connective tissue (ligaments, tendons, muscles), is at its most flexible and elastic when it's warm. So warm up, stretch and generate some body heat before you play.
Hope this helps you. \m/