Spawners only spawn mobs if you're within 16 blocks of them. this can be through walls etc. Mobs will spawn if you are between 24 and 144 blocks away from them.
If you edited in spawners, make sure you're within range of them (they should light up)
The Problem will be that you're more than 16 blocks away from the spawners.
But you said, "Mobs will spawn if you are between 24 and 144 blocks away from them." My main house is like around 30 blocks away from my XP Farm. So, basically the mobs have to spawn normally when I'm in my house right? But it doesn't...
The mobs only spawn when I'm in the area, or outside of the area BUT like right beside the wall that surrounds the area.
Images from your design could be useful