You may already have solved this problem, but I have only just seen your post. Having just repaired my series 3 seats, I can confirm that they are different from the Series Vs. AFAIK all 3s have the seat base and backrest in three parts - the side bolsters and the centre panels are all in separate sections. The support to the centre cushion is provided by crosswise rubber straps which attach to metal hooks. The bottoms of each side bolster are made of a strong cloth with a pocket in it to hold a metal strip. This strip has holes in it for the ends of the metal hooks to locate into. The tension in these straps pulls the upholstery together.
The main difference between the 3 and the V is that the V has a section of frame across the front of the seat to take the hooks to support the rubber diaphragm. This isn't there on the 3, so you can't use the V diaphragm. I think the series IVs have a similar construction to the 3, except the seat cushions and backrests are all in one piece - they certainly use the same type of support straps.
The original straps were made of rubber with metal ends bonded in, but on all the ones I have had, the straps have perished and broken. However, you can buy a woven stretch strapping from an upholstery shop which does the job just as well, although it does look different, so might lose you some concours marks. It comes with toothed metal clips which you clamp on with a vice after cutting the strapping to length (allowing for a bit of stretch). I was told it is better than Pirelli webbing as it lasts longer (and it's cheaper - at least in the UK).
I was lucky with my 3 - the upholstery was in saveable condition, so with new foam and straps the seats are now comfortable again. Much cheaper than paying for a complete recover, and more original as I don't think the proper GT type leather cloth is still available.
Steve