If you have doubts about your tests, then start with stabilizing your testing before you worry about making adjustments. (Instead, just do regular water changes if possible. Add N&P to your new water change water so you don't crash nutrient levels in the process.)
This might sound like "duh" but just practice with the test kit of your choice (don't keep switching) until you get repeatable results. Some kits are easier than others, but most conventional test kits are pretty similar to one another....so the practice will pay you back on all your testing.
E.g. Mix up a fresh batch of seawater (or even test your tapwater; if the Ca level is on your water report you'll even have a target) and test it at least three times in a row. If your results all match, you're done practicing. Otherwise, re-test three more time, and try to figure out what you can do better/correct. I've done this process with any new test kit that's got any level of complexity to it at all....seems to work! I can even get reliable results from the Hanna Calcium meter after practicing. (It's cheaper to practice with conventional kits vs Hanna.)
Once you're confident in your test results you can make more specific adjustments (eg) to Ca and Mg.
I don't think you really have to do anything to make a pod refugium.....everything in the tank should be a pod refugium unless you're running a strange aquascape with minimal cover.
More water/more flow is the concept...taking these things out is like reclamation. In the case of bio media, you're improving the quantity of water more than you're making a relevant improvement to flow...and more importantly you're giving your corals more priority to the available N in the system (by removing bio-mass; but specifically bio-mass that's oxidizing N at a high rate...so very targeted).
Just speculating....lots of things can go wrong. If the system's PO4 levels were that high at the time the temperature was elevated, then I would just not suspect temperature as the cause.
PO4 is pretty much always from feeding....the question is about uptake. Having such low levels of N available might be limiting phosphate uptake for some organisms (anywhere n&p are needed together).
Going forward I would consider dosing some form of N until you regularly see ≥ 5 ppm NO3 in testing....if removing excess filtration doesn't do that for you.
Well, unless you have a large, established reef, a Mandarin is going to deplete your system of pods. It's a given – Mandarins are good at what they do! I don't think phyto will make any difference.
So either save the Mandarine for (way) later, or....
Do the new live rock and do add pods, but also consider some of
@Paul B 's ideas on feeding: For example, he hatches baby brine shrimp and feeds them all the time. (Pretty easy his way.....his book is great too, BTW, if you like his ideas. But check out his posts on his DIY hatchery and DIY feeding thingy.) But he does other live foods too. You'll need some kind of regular supplementation.
Return flow probably isn't a significant factor in overall flow, but it can be very crucial if corals are growing near the return outlet – it's can be a regular source of detritus if you don't to mechanical filtration! Food!!!
Skinny tanks are definitely a challenge – another factor (like grown-out corals) that might necessitate more flow than "average".
Certainly make the most of the pumps you have first. If you're using "wave modes" or anything like that, the unspoken side effect is that the pump is spending A LOT of time NOT at 100% flow. Consider programming less (or zero) off time and see how that works out.
Try minor variations in pump placement. But also try totally switching up the placement of your pumps to see if that helps. Try all pumps on one side of the tank. Try all of them on the back. Etc. Make sure you've tried everything that could make sense. In case it helps: Open spaces are where you create whole-tank flow; if the tank is so crowded there are no significant open spaces then you'll have to add more pumps directly for areas of low flow. (Much smaller pumps can be used, but you end up needing a lot of them. Whole-tank flow is MUCH better/simpler/cheaper.)
But adding another (or upgrading a) pump might be what it takes. (E.g. a Tunze 6020/6040 will fit into places not many pumps will fit.) 4 pumps is not "too many". It takes what it takes...mostly being dictated by your corals choices and tank layout.
Probably the last choice you want to consider, but removing stuff from the tank to make more room (for flow) is a legitimate option too.