Either morale effect is too great/game is too easy
I have recently gained three successive promotions with Woking from BSS to League 1 often by big margins from those outside promotion contention, and am not faring too badly in League 1. This isn't a brag, I'm pretty bored of the save because I'm not doing anything, even changing my tactics (4-4-2, Standard, Long ball, pressing) home or away, or against better/worse opposition. I do not make massive improvements to my squad (or cheat), and only scout using scouts/assistant reccommendations. I managed to land some pretty great players like Lee Hendrie, Francis Jeffers and Kayode Odejayi while in BSS/BSP who banged in goals for me, but every season my squad has been easily able to compete
My history in FM has been pretty shocking until this save, so I can only assume it is down my morale always being superb, the game being too easy or the fact that I can sign **** hot players in the BSS.
It's true, the budgets down there aren't that bad and you can get some really good players as a result. I would suggest you venture into a minor european league (eastern europe, scandinavia, etc) and try that type of LLM if you find it too easy.