How "slow" is a Class T "slow blow" fuse?
Firstly, don't buy critical components from Amazon or Ebay or any other general online retailer. When you need a component that has to meet specific requirements, you need a datasheet. And when you need a datasheet, you need to buy the component from a reputable distributor.

Here's a fuse that I found on Digikey that might be close to what you need: 0298400.ZXH (I didn't actually compare it against the requirements you mentioned, so don't assume it's the right one). The datasheet has these figures that you'll need to study to determine if it meets your requirements:  




If this part fails your requirements, you can use the parametric search tool (which any good electronics distributor will have) to find more fuses and compare their datasheets.