... when I first started perl, whenever I tried to use "my" my program wouldn't work.
It would have been very useful to have explored the reasons why your use of lexical variables wouldn't work. It's not too late to begin!
... packages ... just [seem] more stable.
Package data is global data. Global data is, IMHO, always problematic.
The story goes that during one of the Pearl Harbor attacks on December 7, 1941, General Walter Short, commander of the Army forces in Pearl, was struck in the chest by a spent 50-caliber machinegun round and knocked to the ground. The bullet's impact didn't even break the skin, but when someone picked it up and showed it to Short, he said "It would have been better if it had killed me."
When the day comes (and come it will if it has not already) that you are knocked on your ass by a chunk of global data at the end of a long trajectory from its point of origin, you may have some of the same feelings.