Hello knowledgeable people of the GB&C!

Yesterday I received my Loomis FR 7string from the guitar tech (second one I visited). However I like this guitar I can't make it sound good at the 7th string. The first technician due to radii issues (nut radius and fretboard didnt exactly match) left it with high action (and still much buzzing). At the second guy I visited I stupidly didn't plug in the guitar (someone else was busy making noise at the moment) and though the action and tension (64 for the 7th normal 10s the rest) is pretty good the damn 7th string keeps buzzing.

The buzzing is noticeable while playing through isolating headphones (so I am not hearing the guitar acoustically). When playing clean it's transmitted as it sounds unplugged "DINGtzzzzzzz" It's less noticeable with gain but it really kills the fundamental when you let the notes ring more than 1-2 seconds. Which all sucks donkey balls.

I am starting to get a bit desperate (and paying more and more seems less and less appealing right now). There are no dead frets (I checked all frets 3 by 3 to see) and the buzzing is more prominent the heavier the pick attack is. Could it need fretwork done? There is some slight buzzing on the 6th string (but not noticeable amplified) and the rest of the strings play flawlessly.

Should I try raising the floyd from the bass-side till the buzz stops? It's already tilted that way a bit.

PS: If only someone had a plek-machine in my country
Just spoke with the tech on the phone and I quote: "All 7strings buzz if they are tuned that low with low action" Is he bs-ing me?

Its not a high fret... Even open the 7th string buzzes (keep in mind I am tuned in drop G#) and I checked the frets (with a feeler).

Video is kinda hard now... I ll try later in the day.
I raised the bridge from the bass side about 3 full turns (little by little). Still buzzing all across the 7th and 6th string. Bear in mind that the bridge wasn't sitting flush with the body. After raising it you could see clearly the whole height of its side.

So can I say its a nut issue? Which means that I have to raise it somehow (shim the shelf and rescrew?) Or replace it as a whole? Getting a new floyd nut isn't expensive but I'll have to order from abroad...

ps: Thanks guys
It is :/
Upwards of moderate pick attack the string vibrations make it touch the next fret (or the 1st when played open).

That's why I asked if raising it might fix it.
First tech gave it back with high action and buzzing.

Second tech gave it back with low action and buzzing (kinda worse).

Action right now is at 2mm bass-side and checking the neck (fretting at 1 and where body meets neck) it barely passes the credit card test (it fits snuggly)

That's why I was thinking about the nut being a dud. Cause everything else seems fine...
Business card as in a cardboard paper card not like a credit card eh?

I can make a very thin wooden/aluminum shim if need be (if it's better than a papery one ) what thickness would you suggest?

Thanks alot one more time!
One more observation I made today. If I use a capo on the 1st fret it still buzzes all the way through on the 7th and 6th. Does this indicate something that I missed (trussrod adjustment)?

I ll wait for an answer on this one before proceeding with the shim...

Sorry for being a bother and thanks a lot
Last installment to the thread, so people can see how I dealt with the problem:

After spending 2 days literally assembling and disassembling the guitar (going mad in the process ) I ended up with:

1. 0,1mm copper shim under 7th/6th strings' nut.
2. 0,1mm copper shim under 7th string saddle at the bridge.
3. Floyd almost raised whole at the bass side, 2mm protruding from the tremble side.
4. 64 string for G# (7th) string. Slinkies for the rest.
5. Adjusted the neck for 3/4 turn relief.
6. 2 aftermarket springs (a bit stronger than the originals) for a loose but steady floyd

No more buzzing. Low action. Fine intonation throughout. The end.

Thanks everybody for your help!