USA source for 38mm Pirelli/elastic webbing and clips?  

Timely question, as I just came across this situation yesterday. I have slots on two PJeppesen lounge chairs that look to have been made for 38mm straps. I tested passing a 2" Elasabelt strap through the slot yesterday. While the slot is slightly narrower than the strap, the elastic nature of the strap allows it to compress within the slot depth. In my case, a single strap will zig-zag back and forth for the seat support, so the resistance between strap and slot will actually help me maintain pre-tension as I thread the strap. The resistance is enough that I may need to use pliers to pull the strap while installing.
I can't verify yet that this will work perfectly, as it was only a test run yesterday. However, I plan on stringing them up over the next couple of weeks, in time to receive the Hallingdal covered cushions currently being made for them. I will follow up in this post afterwards.

I appreciate the feedback.
I've also contemplated simply cutting the 2" webbing and clips down to size. Since the webbing itself appears to be cut to width at the factory, I see no issue cutting an extra 25mm off. For the clips, cutting them down would surely compromise the zinc or galv coating, but that's a small issue for a piece living in a climate controlled home. Both seem to be very tangible solutions, but here's the thing ... while I have no issues spending 40-60 hours sanding and oiling a piece, I hate hate hate spending time on something when I know there is an off-the-shelf solution.

Two more comments:
1) I would not recommend trying to cut an edge off of Elasabelt material. It will start fraying almost immediately. Never tried doing that with Pirelli straps.
2) Which clips are you referring to? It's hard to tell from your photos, but it appears that the slots in your seat frame are meant for the straps to pass through. The clips I have worked with are intended for use in 45 degree grooves in the top side of the seat frame.

The Elasabelt webbing definitely cannot be cut as it is woven to a specific width. Unlike the Elasabelt stuffs, the Pirelli webbing appears to be produced by encasing a woven mesh with rubber, then cutting to width. One can assume (perhaps wrongly) that the 38 and 50mm webbing is the same material, simply cut to differing widths.
As for the clips, there are two types: a 90 degree version and a 45 degree version. The 45 degree is used on Fagas style slots. The 90 degree version appears to be used most commonly in vertical milled slots (there are some Seligs like this, prior to them utilizing Fagas style straps).

Now I'm not so sure about those 90 degree clips, at least for this chair.
I found a picture online posted by a respected reseller of what appears to be a mostly original specimen and it looks as though the webbing is wedged into place somehow. I say "mostly original" because I'm certain the chair original lly had button head caps to trim the hardware holes, and NOT contrasting flush mount plugs as shown on their piece. Hmmmmm...
http://www.danish-homestore.com/acatalog/Hovmand_Olsen_armchair_teak_mog...

Finally got around to strapping the PJeppesen chair and it went fairly smoothly. Didn't need to use pliers as pulling, and tensioning by hand worked fine. The tension between wider strap and narrower slot did help with maintaining pretension for each run.

For those looking for Pirelli webbing, the current distributor is located in England. Their contact information is below. I don't know if they sell clips as well.
Handy Ltd Office
Unit 9, Sovereign Business Centre
Stockings water Lane
Middlesex
EN3 7JX
By Appointment Only
Tel: +44 (0) 20 8805 8050
Fax: +44 (0) 20 8805 8055
Email: enquiries@handyltd.co.uk
Web: www.handyltd.co.uk
I don't know if they sell small lengths, but an email to them should answer that question.
The actual manufacturer is Dellner Woodville Ltd. in Swadlincote, Great Britain.