Niallmac, IMO the seat in the repair kit photo looks the same as the seat in your photo. I think if you removed the needle valve and the inlet screen from the assembly in your photo, you will see that the two look the same.
The repair kits are tricky. There are a lot of posts on this forum reporting less than stellar results from repair kits purchased on eBay, Amazon, etc. Although the genuine Suzuki parts are astronomically expensive, they seem to be your best bet for success. This post should prove useful. It will tell you what to look for regarding the repair kits. It's not all-inclusive, but it will get you headed in the right direction. I can tell you that the seat I received in the "All About Carbs" kit is dimensionally identical to the illustration you provided. Only thing I can't verify is the diameter of the feed hole in your seat. BTW, the "All About Carbs" kit was totally bogus junk.
http://suzukisavage.com/cgi-bin/YaBB.pl?num=1641171298You reported that your slide needle was stuck in the needle jet. You stated that the needle had
"a 3mm wide circle of glue-like film". Based on your video, it looks to me like the needle was indeed glued to the needle jet. That most certainly indicates that your needle jet is fouled with fuel deposits. There are eight small emulsions holes in the needle jet, and I suspect yours are all plugged with goo. Can you remove your needle jet and post a photo?
Cleaning the needle jet is difficult. Almost nothing cuts these fuel deposits. Mechanical cleaning is risky. The .121" hole (orifice) through the center of the needle jet is critical to correct performance. Cleaning it with any sort of abrasive is risky. The needle jets come in .0002" increments (that's .005mm). It's easy to ruin the jet with abrassive cleaning implements. I have found that PineSol will soften the stuff but doesn't dissolve it. If you soak it in PineSol for a few days you might be able to then scrub it out with a soft implement (like a Q-Tip or a small nylon brush).
Post some more pics so we can see what you are wrestling with.
Good luck.