for the amount of taps, batches to filter will be around 1 gallon at a time.
you will loss a lot of syrup by using a Filter press, (you can wash with hot water and return to boil), i think the best is a cone filter.
Myself i filter two times, i pour the nearby syrup from the evaporator in a polyester cone filter (synthetic), and put the SSpot on a propane stove to achieve the perfect density (5-10min of boiling). after i used an orlon filter to get the sparkling clean syrup ready to be bottled. i never, never ad any settling in my syrup.

You could rince the outside of your orlon cone filters in the boiling sap, to dissolve remaining syrup, no loss.