How to soften new sheets

I bought some new sheets recently, ran them through a regular wash cycle before putting them on our bed, and immediately thought, wait, did I accidentally buy a negative thread count? They were so stiff and almost scratchy. After doing some hunting online, I did the following:

• Washed them on the hottest setting
• Used no detergent (the idea is that new sheets have chemicals on them and detergent just makes it worse)
• Added lots of fabric softener
• Dumped in a cup or so of baking soda during the wash cycle
• Took them out of the dryer as soon as they were dry, rather than leaving them to sit in there for a while

They came out about a thousand times softer, I couldn’t believe it. Plus, the baking soda made them smell really fresh and clean and nice. I’ve also read that you can add a cup of white vinegar during the rinse cycle to help break down residues, but I haven’t tried this yet.