Since its low temp leak, could you pull the fan and run it and check??? Would that cause any issues on a 04? It would take forever to get hot and you could run an external shop fan. This way the airflow is not spraying the leak everywhere.
If you have the budget Mr Bob's has IMO the best set of hoses going.
https://www.mrbobsdistributing.com/dodge.htm
I dont see how just filling the bottle would make it 10x worse at low temps unless the bottle is cracked or something, the coolant is just sitting in the bottle. Unless the entire "system" leaks to such a low level below where the Rad is broken, and they refilled the "system" above the leak.
On the line of odd coolant leak stories...
For 3+ years several oil change place including one dealer would tell me my '11 Traverse had a coolant leak, bottle would be empty by the time I was due again for oil change, you could smell coolant once in a while but no leaks on driveway ever. It never ran hot, pressure tested several times nothing showed up. Finally I figured I needed to do some research on good ol'Google, turns out that specific bottle has a "FULL COLD" in large letters at the top, so folks fill it to that level, what they fail to notice is the small arrow from that word that is about 6" long down to the bottom of the bottle, it only hold a few oz of coolant, when you fill to the top it spills out when you make a turn, eventually gets to a lower level where it never spills out, then the next person would fill to 6" above the real line and repeated the process, so there was never a leak but it would smell since it was spilling out.
Pic from another forum.....