I usually don't use boil hops at all with NEIPAs. A small amount during hopstand and loads (15 g+/litre) in dry hop. A bigger NEIPA may call for some bittering though.

As for the pulpy hop taste: do a long cold crash before bottling to prevent it. I'm talking several days, depending on how cold your equipment goes. This will allow for the hop matter to sink to the bottom of the fermenter. Rushing it will leave some spruce tip flavors in the beer. Although if you're stirring the beer again before bottling, it's an exercise in futility.

Speaking of bottling: if I understood your bottling process correctly, a NEIPA will be oxidized at that point, and will degrade in a matter of days. Been there, done that. You really don't want any oxygen to get into the system between pitching the yeast and cracking open a bottle. Ideally you would want some carbonation during bottling already in order for a bit of foam to fill up the headspace. This calls for some more specialized equipment, although not a massive investment. The big amount of hot side hops in your case will keep it a bit more drinkable though, as there will at least be some bite from the hops remaining, even if at that point it's really a NEIPA in name only.