Installing elasbelt black elastic webbing  

gropius, why do you say that these V-clips were not designed for this purpose? I thought they were designed just for this purpose. They are a flexible low-cost alternative to Fagas straps, which have to be factory-made to size. These clips work with both elasabelt and PIrelli webbing. I can certainly understand certain owners wanting to use close-to-original materials and designs for replacement pieces. However, there are many generic vintage chairs out there with groove slots that may not be worth the cost of using Fagas straps.
I agree that widening the groove is not a good idea.

I'm not being argumentative, but if you don't like the idea of widening the groove then that's why you should use a Fagas strap - or a compatible clip. The Fagas straps have a single layer of metal that goes into the groove - which is why the grooves are so narrow. But the clips that I used in a non-Fagas strap chair and that powbum is trying to use, has two layers of metal plus a layer of rubber strap. It is simply too thick to fit easily (if at all) into a Fagas strap slot, but it fits perfectly in the wide slots in my chair.
These two systems - the Fagas strap clip and the one on my chair (I'll call it a Varkala clip since he took out the patent) are not compatible or interchangeable. Chairs back in the day used one or the other. You may be able to make them work if you try hard enough or bend the clip or widen the groove, etc. But at the end of the day its a hack.

When I used these clips with elasbelt, I had to bend them for a 45 degree angled slot, and I had to pound them thinner with a hammer so they would fit in the slot.  No widening of the slot needed.  Perhaps there are cases where even this would not be sufficient, but a hammer and anvil will make the clip a lot thinner than it was before.

I have had chairs with grooves that were so narrow that no amount of hammering could make the aforementioned style clips fit into them.  I know, I tried. (And tried and tried and tried.)
 

An anvil? Are you kidding Leif? Who owns an anvil?
Okay, I do. A sweet little Fisher 50-pounder cast in 1908 that I snagged at an out-of-the-way junk shop more than 20 years ago for 50 cents/lb. I use it regularly, too. Got a Stanley Bailey #7C maybe 30 years younger there the same day, rosewood tote fully intact and most of the decal still on it. I hardly ever use that one, but it filled an empty slot in my plane collection and, again, $25! I felt like a lucky man that day.
Sorry to brag there a little. So few people I know anymore could appreciate these things much less care.
Really, Leif. A Zappa fan AND an anvil owner? Your wife must be a saint.

Yep. I use the anvil a lot. It is actually my grandfather's anvil. It is only a small bit of an entire forge that is in my future. Including such wonders as a vise that is half as tall as myself. 
And I have his Papa Bear. 
These are important things

And she is a saint. Better than a saint.