Three strands probably wouldn’t do anything flavor wise. The recipe calls for 1/4 teaspoon of saffron threads. I assure you it doesn’t overpower the dish. It adds just a hint of smokiness to the arroz con pollo.
I am wondering if the saffron you bought picked up the scent and the flavor of something it was kept near at the store or perhaps in a warehouse before it go to you. Some foods including some spices will pick up the taste of something with a strong scent that is stored nearby. I won’t even let them put any cleaning products in the same sack as any food items I am purchasing at the grocery store for that very reason.
My saffron does not smell or taste anything like bleach. I had everyone in my house smell it and taste it and tell me what they thought of it. They all had a similar comments to mine. My daughters both thought it had a faint smoky taste and smell like beef jerky. The guys thought it had a slight smokey barbeque flavor like the crust you can get on meat cooked on the barbecue.
Considering I didn't like the taste I think I'll refrain from using 'more'. I'd hate to ruin a whole pot of something.