Suggestions For Slightly Bigger Fish

So we are talking about a 240 litre, 120 cm long tank and very soft water (31 ppm, 1.7 dH)

First of all, yes, get some more cories. You do have plenty room in that sized tank! Adding to a shoal of cories is not a problem as they are just about the least hierarchical, least territorial fish we can buy. (Tip - skunk cories are not in the database on here, so use panda cories in the community creator at the rate of 1.5 panda per shunk, as skunks are bigger than pandas, so for your current 5 skunks use 8 pandas)

Harlequins and rummies are not as small as, say, neon tetras, so how about pearl gouramis, 1 m 2 f? I know the CC says they shouldn't be kept with harlies and rummies but they should be fine - that's just a note of caution, not that they definitley will eat the smaller fish. Pearls are a lot less aggressive than the three spot gourami in all its colours (opaline, gold etc)
Or Bolivian rams, which grow bigger than rams (in all their colours - blue, german blue, gold, electric blue etc)?
Or a species of Apistogramma? Male cockatoo cichlids (A. cacatuoides) get quite big.

The last two, being cichlids, do need to choose their own mates. If you decide on a cichlid, I can tell you how to chose a bonded pair from a shop tank.

Bare (bear?) in mind that if a pair of cichlids breeds, and if it's a compatible pair they probably will, then they will defend their kids against all comers, which will not be tolerated anywhere near them. And you'll have to feed the fry(?)

Pearl Gouramies are a good choice. They're nowhere near big enough to eat a fish the size of a Neon, since they have a very small mouth (and are not fish-eaters anyway). They are quite a shy fish though and like dense planting, and not a strong current. They're worth it though, very beautiful fish once they're fully mature.

Do you want just one or two bigger fish or a group? You could go for a group of Dwarf Rainbows, African Red-Eyed Tetras, or many others that are not coming to mind (I've just done a 17 hour shift largely because of snow, and need to sleep).

For cichlids how about Laetacara (dorsigera, curviceps... very peaceful), Keyholes...

A couple more to add to your list!...

Kribensis?
Angelfish?

Five band barbs should be fine. Gouramis are sedate fish with long dangly fins (their feelers). They do not mix well with nippy fish (the feelers) or active fish (eg barbs) though 5 bands do seem to be among the more sedate barbs so they should be OK if you decide to get gouramis.

Always check on the behaviour of a species on Seriously Fish before buying

I usually fail to find it as well. I resort to googling "seriously fish pentazona" and that finds it.

Fish names change. Usually it is the genus name, the species part doesn't usually change. If a search on SF fails to find the full name, I search with just the species name - pentazona in this case. But occasionally even that doesn't work. Searching for pentazona just gets Puntigrus tetrazona, the tiger barb. So then I use google (well, duckduckgo to be precise), and type in the website name followed by the species name. That works for 5 band barbs 

There are actually 3 fish commonly sold as pentazona barbs. Desmopuntius pentazona, D. hexazona (not as easy to distinguish as their names suggest) and Puntigrus partipentazona. The Puntigrus genus (the Tiger Barb genus) has a higher body.

I agree they're a good choice. They're not nippy and tend to stay in the bottom half, ideal for Gouramies, who tend to prefer the top half.