The other of the three on that side of the yard, the one closest to the brick wall, has a little tiny bit of the same issue but it's growing like crazy and budding out rapidly already.

See photo of the other. The red bumps are new branches sprouting out.

That's what leads me to believe there may be a slight iron deficiency there.

Bump.

Your photinia is suffering from salt burn. The leaf edge necrosis gives it away. Iron deficiency results in a pale green leaf with prominent veins.

You'll need to deep water your shrub, if possible, to wash the salt accumulation out of the root zone.

You can add a filter to the hose bib to greatly reduce the salt. . From another thread:

The filters do mitigate salts pretty well - all heavy minerals. I have great success with them. I water a few herbs along with the veggies, which act as indicators for my water quality. Lemon balm and basil will show leaf burn, and that's when I know my filters have be changed. But generally, the filters last about 3-4 months on the daily water stuff. These are my super-duper secret weapon in the veggie garden.

I usually get them at HomeDepot ($10) but they carry them only during warm season. Find them with the misting systems. I buy a batch for the year so I don't run out over winter

You may be able to get them at some irrigation supply places (Sprinkler World, Ewing).

Hope this helps!

Here is a link that might be useful: Particle Filter

Someone told me that Epsom Salt reduces salinity. Any thoughts?

What about gypsum?

Epsom salts will add magnesium to the soil. It won't reduce salinity. Epsom salts are also incredibly alkaline, so they should be used sparingly in our soil.

Gypsum will reduce sodium levels, particularly in soils that are mostly clay and do not drain well. However, it's not a cure-all for salt burn.

Great. I've tried pruning all the damaged stems (and have them in mycorrhizae fungi propagating), and more heavily irrigating the planting hole. I think the salinity is not actually coming from the hole itself but run off from the soil closer to the house. My yard is on an, about, 25 deg. decline from the house in an urban neighborhood.

When in disturbed soil from uphill erodes toward the hole, this would trigger increased salts to the roots of plants below, correct?

I'm going to buy some gypsum this week. Just lay it on top and water it in, or should I attempt to dissolve as much of it as possible in a watering can, or should I dig up some of the soil and amend with gypsum. I've also begun watering with ultragreen root starter solution to revigorate the roots (although I think it contains some salt-based ingredients, and may amount to snake oil).

Any other suggestions or should I just let nature takes its course? If the photinias don't end up growing properly can you recommend some equally pretty but thick shrubs to serve as a privacy screen? We have photinias at my work that grow like crazy, and they're planted right next to a wash; so, I figured it'd be an easy win.

Thanks!

You don't really need that much gypsum for a shrub that big. At most a 1/4-1/2 cup distributed along the outer edge of the photinia bush. The key thing is to water it in and then proceed to water deeply once a week until your symptoms improve.

If the problems still persist and you still want a photinia, you'll need to dig up the plant temporarily, dig out a decent size hole, and backfill with heavily amended soil or potting soil. Other options for shade screens include oleander, arizona rosewood, texas olive, and tecoma shrubs like yellow bells/orange bells -- the latter being frost tender, but do come back with a vengeance every spring.