Rosemary and lavender are Mediterranean herbs. They like dry and gravelly soil. Plant them in Gritty and you'll get better results. Thyme and sage like these conditions too.

My guess is you overwatered and kept them too wet. 5-1-1 can be overwatered. Gritty nearly cannot. You will have to water Gritty everyday for the first week or so, then you can taper off and water your herbs probably every 3-5 days.

I find 6" plants are too difficult for me to put into 5-1-1 or Gritty. They don't really have a solid root ball. Ideally, you want to get rid of all the old soil off the roots before you transplant, but doing so on a young delicate plant can damage/remove a lot of the root structure/fibers. Plus more damaged/missing roots means less anchorage/stability when planted. Can you buy 1-gal plants?

A properly-performed transplant might make a plant sulk for a few weeks or drop some leaves/blossoms, but it doesn't usually cause shock or death. If anything, once a plant realizes it's in a healthy 5-1-1/Gritty environment, it perks up after a week or two and often explodes with new growth.

Those herbs LOVE alkaline soil ( pH of 7 +) and very little nutrients.
Technically, 511 should be fine as far as drainage is concerned. But then the question is pH level.

JMO

Thank you, Oxboy, your advice rings true to me. None of the little guys had a solid rootball, and it was difficult to get the old soil off the roots. I think I should not buy such small, delicate plants from now on.