I have a few ideas to try.
Why use warm water for soaking? Why not cold? I would go for a longer soak too, probably overnight, honestly. I would rinse and change the water until it is clear (or pretty near to clear) and then store in the walk in overnight. I've heard of people soaking in an acidulated water bath to toughen the pectin (which I imagine would allow for a longer cook=crispier, but I've never tried it)
Are you putting your fries in the plastic tub straight from the fryer on the blanch? Then straight to the walk in? If you're piling on parcooked french fries on top of each other then putting them hot in the walk in, they would still cook/steam and that might mess up your texture. Maybe try draining them on towels or on a sheetpan/rack, cooling to room temp and then storing in the walk in.
Maybe try reducing the initial fry from 350 down to 325 or maybe even 300.
What temp are you frying at for the second fry? 375 might be better if you're doing it at 350.
I'll add an additional opinion of mine, YMMV. Most places that make their own french fries have sucky fries. There are restaurants that make homemade fries that are amazing, for sure, but I would say as an aggregate, most places with house made fries suck. Soggy, limp, oily, under-seasoned, I could go on.
One of the very very few things I (usually, at least) advocate for buying a prepared product is french fries. Most of the reputable french fry companies use specific types of potato that they sort and grade so that they don't have "bad" potatoes in their batches (McDonald's does this the best, probably...they have an insanely stringent regimen for potato/fry production) and that the potatoes they use are the best types for fries. You could get a batch of potatoes from your purveyor that are too starchy, or too sugary, or too wet, or too dry, or old, too spotty, too bruised...etc. You can do everything right and still get sucky fries, because you had sucky potatoes. So unless you know how to choose the best potatoes, and store them...
A perfectly cooked, hot, crispy frozen fry (bought in) is infinitely better than a limp, soggy house made one. A properly made hot, crispy house made is best, but those are few and far between in my experience.
One of the hardest parts too is that everyone has an opinion about how to make fries, there are literally dozens of "best" ways to make them. It's tough to sort through all that info.