The banana odor and the oiliness would seem to be two separate problems.
The oiliness would likely be be a particular strain of the lactic acid bacteria. Even though you used metabisulfite, cider’s high pH makes it necessary to increase the dose you use in order to insure an adequate amount of free SO2.
When it does happen, the oiliness should be treated as is noted on various websites for “ropiness” or “oiliness” from lactic acid bacteria . SO2 and a reduction in pH and some method of forcing the “oiliness” back into the cider.
As far as cider sickness ... it does seem odd that you would have the problem with no residual sugar and getting the problem and right out of the primary like you say.
That cider.org.uk site is easy to read. If you want another site that will help you get to sleep at night ...
Everything you always wanted to know about zymomonas but were afraid to ask ...
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC413995/?page=1
If it is cider sickness, the hot ticket would seem to be to make sure your pH is always below 3.6, always ferment to dry, and use scrupulous sanitation on everything to avoid contamination.
If however it is not cider disease and just an issue of one of the acetates, then I’ll take another stab at it.
Right off the bat, let me go out on a apple limb ... because you used apples from your orchard and from your description it sounds, grind and press them before having given them a good bath in sulfites (before the skins are perforated) ... you may still have non-saccharomyces yeast that has taken hold. And consider too that because cider has a higher pH, your eventual metabisulfite additions might not be high enough to combat it (you need extra metabisulfite in high pH musts).
Normally the hard and fast way to check what yeasts are present or winning the battle is to just put a bit of the must under a microscope and observe the shapes of the yeasties ... this is probably not an option here though so on to more guessing ...
Banana odor usually is describing (iso) amyl acetate.
The production of this ester is usually not a problem, however if it is overdone it is still a wine fault. In apples, I would look at two things IF this is the issue ... 1) is your primary fermenting done under airlock or at least restricted such as a carboy without airlock ... and ... 2) is the fermentation temp on the cool side? Both of these increase the production of iso amyl acetate.
Though a problem with amyl acetate is somewhat unlikely ... if you were fermenting in a fairly oxygen deprived environment (as noted above), and consequently the over-production of amyl acetate was in fact the problem ... then next time I would use a bucket primary fermenter with only a cloth over the top. Also, if the temp during fermentation is a bit on the cool side ... maybe raise the temp (a bit up the recommended range for that yeast) to reduce the amount of CO2 in the must.
To be honest though, the more common problem would be another kissing cousin in the acetyltransferase family ... that is the production of Ethyl acetate (rather than the amyl acetate).
This is often described as a “nail polish remover” smell. And though it does not sound exactly like what you are describing, this is a much more common fault.
With Ethyl acetate ... first, the sulfiting should have helped prevent it. Sulfiting helps with avoiding (wild) non-saccharomyces yeasts which can cause it ..... it helps with too much oxygenation {([ETOH + O2 = acetaldehyde] + O2 = acetic acid)+ ETOH= ethyl acetate}..... and it helps with acetobacter or other bacterial infection which can cause ethyl acetate.
Another thing that can produce ethyl acetate ... yeast under stress.
You said that you used a Cote d blanc ... this is not the hand-to-hand fighter that some yeasts are, and also is a yeast that needs nutrients ... and cider is not known for its natural nutrients.
Pasteur champagne is much better in low nutrient environment and is a stronger yeast.
If nail polish seems to be the note, especially also if the cider seems a bit vinegary too ... and you did ferment in an open bucket or had too much in the way of exposure to oxygen ... this could be the culprit. The correction is to avoid oxygen exposure during fermentation, especially in the secondary and beyond.
I’d keep with the champagne yeast rather than the cote d blanc ... and if cote d blanc - use a nutrient like DAP. (actually if it were me I’d use K1-V1116)
I’d also give the apples a soak in K-meta or somesuch prior to grinding them.
And of course ... strict sanitation.
Just some ideas ... but just guessing at the problem. Hope it helps.