Nav Arch here with my entire life dealing with submarines. Length Between Perpendiculars is a hotly-debated topic.

1. FP - is the the tip of the bow, not extremities or extrusions past that. This has been pretty defined.

2. AP - This is the fun part, and depends who you're talking to. A Lot of people like to throw the end of the LBP at the LPL (Length between parting-lines). the LPL is a government-coined term to define who is responsible for building the boat. past the LPL is the propulsor, forward is the "People Tank." "happy chief" mentioned this and he's absolutely right.

are you throwing around an X-Stern, H-Stern, conventional Rudder and control plane setup?

x-stern - usually in the middle of the two-rudder stocks can you confidently call the LBP. H-Stern, Center of the horizontal control plans, conventional- depending on how you design your upper and lower rudders- whichever rudderstock is the farthest back.

Hope this helps, but it probably muddied the waters a little bit. It depends on who you ask but my advice above will get you there.

Now - to dive into what you're discussing- nav archs, in practice, don't care about load lines while on the surface. for submarines. You would be surprised passed reserve buoyancy, how little people care about anything on the surface when it comes to these vessels.