@hansonian
Just to clarify ...
Your primary fermentation is fine in the primary bucket-fermenter.
Particularly with all the SO2 in the must now (assuming you added it), this is best done with no lid on top and just a cloth over it to keep debris out.
If you really want to do the primary fermentation in the carboy you could try it but you may have problems with things like overflow or the yeast having trouble getting going. If that's the case you'll find out soon enough.
Once your primary fermentation is mostly complete (about 5 days ... or as tested by hydrometer) ... rack it to the glass carboy you have, eliminate any headspace, and put the airlock on.
Your description of the wine having “a different viscosity” sounds a bit like a lactic acid bacteria issue, if that turns out to be the case ... and even if not ... a few more comments.
If your kit did in fact come with EC-1118 as rawlus suggested it might, that is a good yeast for you to have in these circumstances (it is also a good one to pick up if you are going to go buy fresh yeast separately).
EC-1118 or “prise de mousse” has a good “competitive factor” and will make it tough on bacteria such as lactic acid strains.
It is also a high SO2 producer (yup, yeasts actually produce their own sulfites or SO2) which will further inhibit bacteria; and 1118 is tolerant of higher sulfite levels in general ... such as any added campden tablets or other metabisulfite products ... making it less sensitive to all those campden tablets you might have added. (like yooper said, about 2 campden tablets per gallon)
Determining and stabilizing the pH of the wine would be a very good idea.
If you have any pH test strips, your wine should have a pH no higher than 3.5. (3.4 to 3.5 is a good target)
Lowering a higher pH would be done with the very careful addition of tartaric acid at the end of active fermentation ... but sooner as one of the things you do if you start getting *any* spoilage growth, mold’ish things etc. This “end of active fermentation” is when your wine has fermented to dry ... or if you do not have a hydrometer, when there is no more activity in the air lock on the carboy.
I suggest to wait until after active fermentation to adjust so that any natural pH change will have been played out and you will have a stable wine to test and possibly adjust.
While the type of lactic acid bacteria that causes the viscosity issue (aka “oilyness”
would likely be the leuconostoc strain which is a bit more tolerant of a low’ish pH, none the less the lower pH will insure a greater amount of free sulfites (basically the “active sulfites”
remain available in the wine must, and as well will work against potential spoilage bacteria generally.
Regarding the viscosity issue ... there are specific ways of treating that specific type of lactic acid bacteria problem IF you have one. The process involves stopping the bacteria with sulfites, forcing or whipping the more viscous part of the wine back into the rest of the volume, and filtering. Of course if you do not have an expensive wine filter then you will not be able to do the filtering part. In any regard, stopping the infection by campden/sulfites and keeping the proper pH are the most important things to saving the wine.
A higher alcohol level (ABV%) is desirable as ethanol is inhibitory or toxic to lactic acid bacteria and other spoilage organisms. If it was me, I would have increased the sugar content as necessary so that the wine ferments out to at least 14%. Another layer of protection.
Once the wine is done and bottled (or put in its storage jugs etc), store it in a cool’ish spot ... say, 50 to 60 degrees ... with little temperature changes if possible ... and out of the light - even if that just means covered with a blanket.
Finally, this might be a batch you begin drinking sooner rather than a lot later. At least opening a bottle regularly to check (ah, drink) it for any developing problems.
While it is possible that any spoilage organisms might be killed off by the sulfiting (campden), the yeast and fermentation, and the resulting percentage alcohol ... there is a real chance that they will not.
And while it would certainly be nice to keep it for at least the 6 months they suggest ... though the wine might be a bit “young” and “brash”, I’d start enjoying it right away.
Like the Romans said - “protinus vive”.
And by the way ... when you get that new kit ... be sure to wash and sanitize all surfaces and every single piece of equipment that contacted the infected batch to avoid infecting the new batch.