The Hardwood @ 3/8", and the limestone @ 7/16 " is pretty close in thickness. We're talking the limestone at 1/16" thicker , which is good. There's a few ways you can go.
Keep one thing in mind , engineered plank is very stable when it comes to movement. The large majority of the movement, if any, will be in the widths of the planks, and not the ends. Although engineered is very stable, you still want to allow for expansion space as per Armstrong's installation specs. When scribe fitting an area I usually feel comfortable leaving TWICE the recommended expansion space, parallel to that scribed area. I also undercut my door jambs deep. That's just me. There's guys that will net fit engineered wherever, and dont worry about it. It's a judgement call.
That being said .... Usually if you measure a stone or tile floor thickness say at 7/16", most of the time that measurement is not perfectly consistant, along that edge. Plus ofcoarse you have the 1/16" height difference to deal with. What I usually do is leave a grout line width, the same width as the stone, inbetween the stone and the wood. I then grout the space in, with matching grout , mixed with a siliconized latex additive, for bonding and flexibility. This "grouting the wood into the stone" solves the problem of minor height differences, like wer'e talking about, and makes a nice transition. This only works when the stone is higher than the wood, so you can "feather" the grout into the wood, and deal with height variation, accross the stone edge. If the wood was higher , you would see the edge of the wood, not good. If the ends of the planks are going up to the stone, I will install a feature strip, grout width from the stone, and cut the planks to the feature strip, ( I dont think board ends look good against the stone. If you are cutting to a jagged stone edge, leaving a grout width, I will seal the ends of the cut planks with liquid silicone, to prevent moisture from absorbing into the the cut ends, when grouting and maintaining the stone.
That was a mouth full
I hope you understand what I just said !
Let me know if questions
Howard