You probably can. But I would acclimate them carefully, as your pH is higher than is recommended for them. Drip acclimate slowly, as big changes in either water hardness or pH can be a big shock. Neons also turn their glow off at night, and it takes a little while for them to start it again when the lights come on in the morning. Normal for them.
Drip acclimating is not hard, just a bit tedious. But it allows the fish to gradually be exposed to water that's different from what they're already in, without shocking them badly. Most sites say they're ok up to 7.6 or so. They're bred in the millions, so inbreeding and weakness from same is not unusual, but because they are bred on farms, they don't often live in the soft water they originally came from, so they're adapted to somewhat harder water to begin with.
Take it slow and easy, you might be ok with tetras. Most tetras need the same basic water, so I'd drip acclimate any tetra species.
Cardinal tetras are very similar to neons, and may be a better choice. A bit larger when full grown, but they keep their colours better with age and may not be quite as inbred. Difference mainly is neons have a red stripe halfway down the body, Cardinals have it all the way to the tail. Same bright neon blue stripe. The red is like a cardinal's robe in the Catholic church, is how I remember the difference between them.
Danios would be a good choice for your water, there are several quite nice ones. Gold zebras are quite bright and lively, upper to mid level swimmers. Pearl danio, not so colourful, a bit bigger. Kyathit danio comes in two forms. Spotted is my fave, bright gold body, big black spots, like a wild cat. Lively, hardy, similar size and shape to Zebras. Glow light danios have an orange stripe that literally looks like a row of tiny LED lights, shows best on dark substrates under lights. Smaller than the Zebra or Kyathit, a bit bigger than Neons.
Pencil fish are another nice one. Beckford's Pencil fish. Females are not too brightly coloured, but males have bright red fins and a red belly patch. Both sexes have a dark side stripe, darker shading above it, but females are paler overall, no red fins. Males do a dominance dance that's great to watch. Never fight, just swim side by side wriggling and dancing at each other. The red patch and fins just glow.. as if lit from inside, it's amazing to see. They need a tank with plenty of plants or other decor to break up sight lines so the boys don't see each other always. 2 or 3 females to one male is good, two males and five females is great.
Danios do best with a couple of females to one male. If they spawn, which is quite possible, the male who spawns will be faithful to the female, though the females don't care one way or another. If the female dies, the males may choose another. Don't see many fry from them unless you try, as they eat their own eggs and fry, as do many egg layers.
Cories would be great bottom fish, or kuhli loaches. Both do best in groups of six or more, and can be hard to sex, especially the loaches. Black kuhli's are not as bright as their striped cousins, but are much more outgoing, out in the day time, often chasing each other in vertical circles like a sort of fishy ferris wheel. Quite entertaining. They all need places to hide, some wood pieces or rocks and plants, and a softer substrate that won't damage their barbels.
Just a few suggestions to think on.
