I have not a lot of time to devote to this right now and will try to be quick. I like your approach of material balance. The only thing faulty about it is that you are mixing dry weight proportions of nutrients and wet weight of poo. Also, when I google what weight of manure ... I only get 1 to 2 lbs of goose manure as the range (lets use 1.5 as the average). Not sure how much forage that is but one should keep in mind that the goose has extracted about half of the energy from the forage to fuel its metabolism. It would make sense that a goose that consumes up to 4 lbs of forage would expel up to 2 lbs of poop. But goose poo is 75% water ... so you need to account for that which will reduce your estimate of phosphorus. Esshup you mentioned several nutrients but in ponds ... usually the limiting nutrient is phosphorus. I think it best to use the phosphorus as the limiting nutrient. If you do a little more research you will find that a typical goose will poo around 1 lb of phosphorus annually. I've seen estimates of 500 to 550 lbs of wet algae for that 1 lb of phosphorus and so I think that is a good number. Let's use it. If the the phosphorus of one goose supports 550 lbs of algae from its yearly poop ... then the poop on a daily basis is:

550/365 days = 1.5 lbs wet algae OR 1.5 lbs wet algae for every 1.5 lbs wet/fresh goose poo (~1 lbs algae/1 lb poo)

so maybe the minimum is 1 lb wet algae and the maximum is 2 lb wet algae for a goose-day depending on how much it poops?

To maintain a bloom ... some fertilize with super-phosphate. The other nutrients (N and K) are in sufficient concentrations and often do not need to be supplemented. When I google how many pounds of Phosphorus are needed annually to fertilize a 1 acre pond ... the answer comes back ... 25 to 50 pounds of phosphorus. So...

If one goose year is 1 lbs of phosphorus, then fertilizing 25 lbs of phosphorus per year is like having 25 geese on your pond every day of the year --- phosphorus wise. That is 9125 goose-days and enough to grow 6.87 tons of wet algae.

Feeding 800 lbs/year of feed with minimum 1% phosphorus ... its like having 8 geese on your pond every day of the year ... but only if it is limited to 1%. If 2% phosphorus, then that would be 16 geese and the potential to grow 4.4 tons of wet algae.

It isn't what we don't know that gives us trouble, it's what we know that ain't so - Will Rogers