I'm not sure about whether the plant's uptake is faster if "starved vs "fat".
It could go either way. My statement of rates is based on what I would consider "fat". Specific plant species may indeed have different rates, but are they that different?
I think this would play a role when you limit a certain nutrient down to the bone. While as a general method, this might not be a good idea(say with species that do not care for low PO4 levels), but for finding tolerances for specific species, this is a good method.
DOP vs SRP is well studied in natural systems. Our kits measure Total PO4. Submersed macrophytes can remove down to 20-50 ppb(not million) but not beyond this range of total PO4.
The study is very well done, I know those involved and have review their work and given feedback. South Florida water management district has the lowest PO4 mandate of any place anywhere I know of. They need water treated to 10ppb. Few things are capable of doing that on large scale. They have considered many options and researched this issues with many millions, many researchers.
DOP can be broken down, and this process is slower and more difficult to measure since as it's brojken down from DOP to SRP by bacterial reminerlization, it's consumed by algae, plants, bacteria etc and rapidly turned into Organically bound PO4 once again.
Much like how much NH4 from fish waste are the plants getting vs the NO3 from KNO3 etc, the same can be said for reminerlized waste from fish for many nutrients including how much CO2 is coming from bacterial respiration etc.
A lower light, higher fish loads, this will play an incresingly large role. So will reminerlizational processes. At lower light, these processes have the time for the bacterial cycling to occur, at higher light, there is not enough time without destablizing the system. This can be delat with by adding NO3, KH2PO4 etc.
You can answer the question, but you need to test both forms of PO4. I know of several ways at getting at this but it's a lot of work I certainly do not plan on doing anytime soon

Theory and natural systems are all we have really to work with. I'm fine with that as long as the studies are about algae, temps in the right range, have plants also, good research.
Yes, N uptake certainly slows as the PO4 drops/limits, this is a cascade effect and the plant becomes co limited.
This is very common with respect to CO2 and NO3 or PO4. Yes, your conclusion is correct about PO4 excess causing NO3/NH4 to be driven down.
But there's going to always be one or more nutrients that will be driven down, be it PO4 or NO3, etc, pick your poison

You still need some source of nutrient supplementation.
But using less light to drive this will reduce the rates of uptake and allow more wiggle room with your chosen method.
If you are a purist, non CO2 tanks are great, no KNO3, CO2, Traces, water changes etc. I have a great tank with this method. I would say it looks better than many CO2 tanks. It also takes longer.
I'm not a big fan of NO3 limitation for color although it will bring the red out of many plants. I've been the King of NO3 crashes, I'm sure a few other folks can attest to this issue for their own tank observations.
As far as the forms of N, I think you have some credence for sure there, I suggested that a few years back on the APD. I'd suggested to have the best color, even certain plant will do better with more fish etc, more reliance on NH4 is needed from a fish waste source.
But why then would a non CO2 tank not have better color than a CO2 enriched tank since the reliance is almost exclusively based on NH4 waste?
Would a lower light tank produce better color also(CO2 enriched)? Since it would allow more NH4 to be removed and less NO3 for it's N needs??
Which observations do want to you consider? I think there are arguements for both sides of this coin.
Still, I feel is correct that better health/color/growth occurs with a higher relative % coming from NH4 than NO3. But this is a tricky thing since it means balance and many folks know NH4 is playing with fire.
I'm not sure it's worth it for most plant folks. Live with some green and have a nice tank or try lowering the light and relying on the fish more.
Many folks are roasting these tanks at 3-5w/gal with PC lighting.
I'd have a tough time quantifying this, but it seems to be true from my perspective/observations.
It also allows you more wiggle room if you forget/neglect the tank and we all do it sometime or another. Not a bad idea generally.
This might be why Amano's plants look pretty good since he adds lots of shrimps(waste) to the tanks, no algae and lots of NH4. It certainly adds a lot more NH4 to a system even if you do not consider their algae eating abilty and simply consider plant growth/color alone.
Still, I've had excellent results with few fish/critters in tanks with good dosing habits. I'd have a tough time showing real differences IME/IMO.
But part of me would like to argue in favor of more fish waste

It is good if you are forgetful.
Take Bob's Gratiola(Limnophila aromatica) for example.
My tank has no fish, just snails and my plants are much redder than his plants and smaller/not as green, so this seems to counter the whole premise, but this is one plant, but there are others like his L repens. Mine are many shades redder yet my biload is dramtically polar opposite of his, yet the health, color etc is much better, the light is also higher.
So the observations I've seen and experienced are different than what I've just argued for

At least for these two red color variable plants. My GH and KH are 5 and 3. PO4 is very high as is my NO3/traces etc.
Looking at plants and ignoring the algae is a critical observation.
I've said many times, as the lighting intensity increases, so does the tank's reliance on inorganic sources, be them CO2, NO3, PO4, Traces, etc in order to keep the balance.
I'm not sure that fish loads are really that significant in health/color etc as you and I have suggested, more important perhaps is simply not running out of anything for long at a given rate. NO3 vs NH4 etc my be less important in practice.
I could argue both sides of this coin.
Regards,
Tom Barr