I have installed 3/4" by 2 1/8" hardwood flooring following the manufacturers instructions leaving 3/4" gap on all sides.
I have a stone hearth with 4 large stones with scalloped rough and uneven edges.





One stone is also a little shorter than the others so the molding as shown below will have gaps,
and would not be easy to glue to the stone.



Any recommendations would be greatly appreciated.

I would picture frame the hearth with matching pre-finished reducer, ( looks like 3/4) , tapering down to the wood, (fastened to the floor with PL 400 urethane adhesive & top nails). Grout the reducer in at the stone with matching siliconized grout.

Yup, surface picture frame and grout the irregular areas. The only time you are gonna see the grout line is when you are standing in the position you were in whilst taking the picture.

Won't the grout be to wet for the wood.
Can I use grey siliconized caulk?

You can use caulk there are some brands that are sanded to match they texture as well as the color of existing grout.

Most grout manufacturers have what they call siliconized grout caulk, (available in all their colors). It comes in a caulking cartridge or tube ,sanded and unsanded. It's used at locations of problem areas, ie: thresholds, backsplashes, shower pans, (where wood floor meets stone), etc.