You're looking at a couple hundred bucks at minimum for something reliable. Even small Peltier Effect chillers ($125-$150) are only going to cool things 5 or 6 degrees F below ambient temperature. That may work for you but they'll be complicated to use with the Spec III & V. I have one on a 20gal tank I have - plumbed into a large AquaClear filter - and it works well... but the ambient temperature in the room is never more than 72/73.
If a fan can't get you cooled down with evaporative cooling to about 70F, then I wouldn't consider shrimp at all. Especially more sensitive species like Crystals. They work out better for some people, of course, but that's not the case 99% of the time - Neos are just easier and more forgiving. Even with Neos - if your parameters could support them - I wouldn't intentionally keep them in a warmer tank. Shortens their lifespan, can exacerbate other problems.
I keep most of my Bee tanks below pH 6 with kH 0 and gH 5. Most of my Pure Red Line Crystals are at a pH of about 6 with the same kH & gH. Low TDS, as well. Wouldn't consider keeping them in tap water at all.
brought up, what's your kH? gH? TDS? Are you using RO/DI water? How long has the tank been set up and how did you initially get the nitrogen cycle going?