Hi Petri,
I have just read your post, so forgive me being slow to reply ... you are probably happily making Methode Ancestrale by now?
I make cider this way most years (for family & friends rather than commercially these days), and have done so for more than 25 years.
My cidermaking is based on what I have been taught by others & my own experience, rather than scientific knowledge or any understanding of chemistry.
So, to get my method out of the way first ... I tend to use early season bittersweets for this, definitely looking to get some high tannin varieties in the mix. Having milled them , I let them sit for 24 hours & then press. The juice goes into stainless steel tanks. I ferment on the natural yeasts. The juice is then allowed to ferment at the natural temperatures of an unheated stone shed. Since the cider is made in late September, it has time to ferment a fair way before winter temperatures slow everything down. If early fermentation is very strong, I may rack (sometimes even twice), which I use as a method of slowing fermentation, and maybe keeping some sweetness in the finished cider. At New Year I would expect it to have dropped to roughly half of its OG (so maybe 1.056 to 1.025ish). In the Midlands of the UK, fermentation will probably continue (if very slowly) throughout the winter. In February, I will be checking fermentation regularly as it picks up again. If it moves on well, I will bottle at around 1.010-1.008 into full-weight Champagne bottles. Then its a waiting game ... test occasionally. The cider should be poured carefully, ideally the whole bottle at once into a number of glasses, watching for the yeast deposit to start to move up towards the neck, at which point stop pouring, so as not to get that in the glass.
I prefer crystal clear cider, and this method should make that (but I see that you may prefer cloudy). The cider will be 'dry' to most people's tastes, but may well be 'medium' in terms of specific gravity, even 'sweet' (see below).
I only recently found out the names "Methode Ancien", "Methode Ancestrale", "Pet-Nat", and of the 3, I prefer Methode Ancestrale, as it speaks of tradition & those who went before us. I believe that 'ancien' can mean both 'old' or 'ancient' (I like), but also 'former' (not the case for me).
So, pretty straightforward cidermaking ... the less you muck with it, the better it be.
One day I would like to add freezing the neck & disgorging to this method, but that is really only for better presentation. No lees/dregs in the bottle, so you can pour with abandon.
***Occasionally, the cider will 'stick' at a much higher SG (anything up to 1.025 in my experience). If the weather is warm enough for fermentation, but it really does not want to progress, I will still bottle it, having waited for a few weeks to check that this really is the case. This makes a weak (maybe 3% alcohol) but wonderful, slightly sweeter cider allowing good fruit flavour, the sweetness balanced by the drier tannin & also the bubbles which 'dry' the flavour. It should be considered as a gift from nature!
***Natural fermentation ... I like to use the natural yeasts. That is how I began making cider, and still think it the way to make the finest ciders. However, I did have problems for a few years. My cider was getting strange sickly-sweet flavours that were really not nice. I threw away 1000s of litres. I meticulously cleaned, or even renewed all equipment, but it kept happening. Finally after maybe 3 years, having ruled out all else, I killed the natural yeasts, and added a bought yeast. I started in a sugar solution & added it to the freshly pressed juice. Bingo, all was good. I added this same yeast for maybe 4 years, and then decided to see if the 'bad' yeast had been driven out of my shed. It seems that it has. My cider has always been good since that time again. My point here is that yeasts build up in a shed, and that the 'natural' fermentation is all about what particular strains are dominant in your premises & on your equipment, maybe even on your apples (although that seems less important to me).
I hope this may be of some use to you. This method makes the cider that I most enjoy drinking.
Gilbert

Testing in mid-winter

Bottling time