Actually not modded HoI3 neutrality system always worked quite well to me, I was always able to drop my neutrality fast if I focused on it and my country wasn't "democratic". With Portugal for example I was able to attack both Spanish Factions by late 1937 and conquer the whole Iberia Peninsula.
As for Black Ice mod, its crazy how hard it is to drop neutrality, tried the same thing and by late 1937 my neutrality dropped almost nothing... so the issue is probably with the mod rather than the vanilla.
It really depends on how that World Tension mechanic works... as far as I understood it will probably block the minors from doing anything until the majors actually raise World Tension, so forget about growing your country borders before 1939 if you are a minor, but this is me speculating.