So here's my problem: when I turn the key and the engine starts, I hear a quick rumble sound somewhere near the dashboard. Occasionally, I hear the water sloshing around behind the dash over on the passenger side when driving. I understand that the sloshing water has something to do with the heater lines or heater matrix. Occasionally when the air conditioning is completely off, I will feel some warm air blowing through the vents. Is this okay?

And what the heck is that rumbling!?

Mileage: little over 90,000.

 

First of all you have air in your coolant system this is why you hear the sloshing water you need to get the air out asap, follow this guide https://landroverforums.com/forum/sh...ad.php?t=23072. The rumbling could be anything, first bleed the cooling system, the rumbling my be attributed to that.

 

If the rumble is only on cold starts then it may be your SAI pump. Next time lift the hood and stand on the passenger side and have someone start the cold engine for you. Your SAI air filter could be falling apart and getting sucked into the electric motor, it's a simple fix.
x2 on bleed your cooling system, that is most import and do that first.