Woof there’s a lot of misinformation in this thread so far.
Sea run cutthroat are semi anadromous, which means they don’t migrate every year. Their migration is driven by food, not reproductive cycles. You will find large sea run cutthroat that have residentialized throughout the entire length of the Trask and its forks from the day trout season opens in late May through the end of it on October 31. The nicest sea run I’ve ever caught was a dozen miles upstream in June. All techniques that catch sea runs work on residents, too, so there’s no need to target one or the other.
While these fish certainly do like Borden’s Specials, it’s one of the two most popular sea run flies sold in the state along with the Reverse Spider. Tying your own variations of classic flies with the hackle collar reversed will be more effective. Be ready to fish traditional methods too, like nymphs or a dry dropper set up. They like them leggy and gaudy.
From September on, it’s an October Caddis game and you should be fishing big bushy dries dead drifted or lightly skated on the surface.
Finally, while sea runs do tend to live in slower, deeper water and undercuts down in the estuary sections, they live in more traditional trout water as you go upstream. You will encounter far more of these fish in pockets and riffles than in deep pools or eddies.
Long story short, yes you will find sea runs well upstream in July and August. You’ll find more after the first rains arrive, but you’ll also have to share space with a lot more anglers. It’s a wash, IMO. You’ll have a great time either way.