Dan - I will first congratulate you for your intellectual curiosity and willingness to put some effort into experimentation. Many of the protagonists/antagonists of arguments on Reef Central and other reefkeeping sites rely solely on published scientific papers that, because of the author's intent and experimental conditions, have almost no applicability to the argument. Yet these same papers are still cited as "proof".
With respect to your initial experiment, you're correct that there's a basic problem. Phosphorus can exist in many forms and be incorporated into many different molecules. Broadly, you can separate these into inorganic forms (like the orthophosphate ion) and organic forms, where phosphate is incorporated into a bewildering variety of organic compounds (examples include phospholipids, proteins, ATP/ADP, and DNA, and a boatload of other molecules).
That's not an issue if you're asking the question of "how much total phosphorus is in this sample of substrate, whether inorganic or organic", you simply break down the organic forms into inorganic simple phosphates by means of reacting the entire sample with an oxidizing strong acid (nitric is typically used), and quantitate the total amount of phosphorus.
If, however, your goal is to determine how much phosphate is in/on the actual matrix of the substrate in the form of bound/precipitated inorganic phosphorus but excluding phosphorus contributed by organic forms, including whole bacteria, algae, films of absorbed biomolecules, etc..., you have a much more difficult problem. One way of doing this would be to very slightly ablate the outer surface of the substrate particles with a weak concentration of acid in conjunction with copious washing to remove any biofilms/absorbed films of biomolecules, then dissolve the remaining washed substrate in strong acid and quantitate the phosphorus. That's still going to be imprecise, since you're never going to be sure of exactly how much outer surface of the particles you removed, and what amount of inorganic/precipitated phosphate that it contained. But it would at least get you in the ballpark if done carefully.
A few procedural comments about your initial experiment. You're correct that you need to test the hydrochloric acid that you used for its phosphate content, as well as the baking soda. Strong mineral acids will readily become contaminated from materials and equipment used in the production, transportation and storage processes. The industrial/technical grade of hydrochloric acid readily available to hobbyists from pool supply and home stores are often contaminated, at least at a low level, with a variety of metals and other compounds. Really pure mineral acids can be purchased as analytical reagents, but they are quite expensive.
The baking soda will probably not contain much phosphorus if it was produced by the Solvay process. However, there are significant amounts of naturally-occurring deposits of sodium bicarbonate and sodium carbonate (that can be converted to sodium bicarbonate) that are mined on the order of a few million tons a year; these natural sources would potentially contain significant phosphorus (phosphate) concentration as a contaminant.