Huh...I actually use the KIS organics nutrient pack for re-amending, and the NPK is 2.5-3.5-1 (P is the highest).
The last couple runs I've re-amended with 50/50 KIS and Espoma organic tomato tone (3-4-6) to balance the relatively low K and Ca in the KIS stuff.
I hadn't heard about not adding P when re-amending, but I have read about the relationship between mycorrhizal fungi and P in the soil. The fungi are very good at breaking down phosphates and making them available to the plants, like you don't need very much P if you have active, well established mycorrhizae, but too high levels of plant-available P will actually discourage mycorrhizae from growing. So maybe it would make sense to add P in the beginning, then wait until the mycorrhizae have broken it down before adding more... Also probably depends on where the P is coming from in the first place...