Did the watchmaker say which version of the 3313 is inside this watch? Need to know this before I can tell you with any certainty what the issues might be. If not, please PM me the serial number and I will see if the version is listed for this watch on the Omega Extranet.
The 3300 series did have a technical bulletin sent out instructing watchmakers to upgrade certain parts. I can't seem to attach the PDF file, but can email you it if you PM me your email address.
That was years ago. Maybe your watch wasn't serviced and these parts need to be installed while it's being serviced.
Also, I think that's the 2 level co-axial which does have problems with the lubricant on the pallet jewels. The 3 level co-axial, as it was designed by Daniels, doesn't need this lubricant as it's more of a protection against the escape wheel striking the pallet jewel surface (or something like that). I think
@Archer has talked about this once or twice so hopefully he'll reply in this thread.
A bit of clarification is required on this post. There are 2 separate issues in play with this family of movements. One is upgrades to the original Swiss lever versions (so 3301, 3303, etc.), and if the movement was produced say after 2009, then it should already have all of the upgrades made to it. None of these upgrades have anything to do with low balance amplitude, as they are primarily related to the chronograph functions, and one in the winding/setting area. Most of these issues were worked out before the 3313 was made by putting a co-axial escapement in this movement, but a couple of these cross over.
The second issue is the version of the co-axial escapement in the 3313. Now just to be clear, as the post above seems to imply that the 2 level was Omega's baby, both the 2 and 3 level designs were initially designed by Daniels. The 3 level was the original, but when he was shopping this design around to find some company that would buy it, the bigger players who rejected it eventually, said the 3 level design was too thick. Daniels went back and came up with the 2 level design, but those companies still would not bite. Omega used the 2 level in their first co-axial, because it was more easily fitted into the Cal. 1120 movement (ETA 2892 base) than the thicker 3 level was, so the 2500 A was born.
All Omega co-axial escapements require lubrication on the teeth of the co-axial wheel, and this acts as a cushion between those teeth and the jewels of the pallet fork. The difference between the 2 and 3 level designs is that the 2 level can develop a sticky residue between the teeth of the intermediate co-axial wheel, and the co-axial wheel.
This can stop the watch, and although there is a work around, it really is a design issue with the shape of the teeth on the two wheels. The "upgrade" for the 3313 could be a change from the 2 level co-axial version, to the 3 level. Omega supplies a kit on exchange, so the main plate, intermediate co-axial wheel, and the co-axial wheel are all changed - this is how the kit is supplied:
Here are the parts:
And installed in a watch:
You will see that the version of the movement is now a 3313C, when it was a 3313B. So when he says he will upgrade the movement, it could be for the chronograph related parts, or it could be for the escapement version. You should find out which it is - the upgrade for the escapement is not cheap.
Also, the comment by the Omega trained watchmaker (I would ask for proof before I would let them touch your watch) is strange indeed. The entire point of the co-axial is to reduce the frequency of service, so saying it requires more frequent lubrication flies in the face of what Omega is trying to do here.
Oh and edit to add one more thing - if he is quoting the balance amplitude, he needs to have a timing machine that is equipped with a special program that is specifically for the co-axial escapement. This is listed as "Special 1" on the machine's menu, with Special 2 being for the AP escapement. If he is using an older machine (which Omega does accept) that does not have this special program addition, then the balance amplitude numbers will not be valid.
Anyway, hope this helps.
Cheers, Al