Milford Haven was not a parish during the time of your interest but came under Steynton Parish, therefore that is the location I would start. Last time I was there one had to fight through the overgrown brambles tree’s and bushes etc.
Thornton Cemetery did not begin until post 1868, the 1st burial being in the mid 1870’s
You could also search Hubberston, Hakin, Llanstadwell, they are just established church, there is also a number of non-conformist chapels and burial yards you could search in and around the area.
The Act of Churchyard clearance of the late 1860’s saw most old headstones lost from large churchyards with the introduction of out of town cemeteries, so there is limited chance that the headstones you seek will survive. However a number of churchyards sort of ignored the Act so that we are left with some good early headstones.
The alternative is that you look at the census each person appears in prior to their decease and start with that parish churchyard.
Do you have their burial entries, if not I shall be at the R.O. next week and can check Steynton burial register on you behalf if required.
Rgds
Orielbenfro
ORIEL a welsh window on a surname
