Governor games are always weird and fucky because you have to play them by ear so much based on the situation.
Generally with a game where Governor is dominant, you get a lot of Governors, and you use all your other gains on cards that can either mitigate the downsides of Governor or replace one of Governor’s core functions. So you try to add draw, or remodeling, or Gold gaining, so you can save your Governors for the function you have less access to.
Stonemason changes a lot here. It offers a really quick way to get multiple Governors, so you want to hit high cost targets very quickly. I am not sure if Apothecary or Magpie is the way to do that, so I would say Magpie since it can be a lot faster. Magpie for pseudo-draw is a big help here, and later on those Magpie can threaten to become Duchy in a pinch which plays into the end game a bit.
Obviously you grab a Militia at some point, I would actually say fairly early so you can potentially stop some $7 turns, probably the back of the second top of the third shuffle. You can also Remodel an Estate into it with Governor.
Otherwise it is fairly standard Governor fare. There is likely no time for Gladiator. Get a Worker’s Village or two so you can buy more than one thing - ideally Remodel Estates into it. Pilgrimage seems really good if you can time it to get you Magpie Governor and WV or Gold or something.
So my plan: Open Magpie Silver, get a Governor quickly to Remodel those Estates, splash in Militia, Magpie, WV as you can, Stonemason for Governor any time you can, watch those piles.