Hi Michael
The problem you have is the very low value content that exists on all of those pages and the complete impossibility of writing any unique Titles, Descriptions and content. There are just too many of them.
With a footwear client of mine I no indexed a huge slug of tags taking the page count down by about 25% - we saw an immediate 22% increase in organic traffic in the first month. (March 18th 2017 - April 17th 2017) the duplicates were all size and colour related. Since canonicalising (I'm English lol) more content and taking the site from 25,000 pages to around 15,000 the site is now 76% ahead of last year for organics. This is real measurable change.
Now the arguments:
Canonicalisation
How are you going to canonicalise 10,000+ pages ? unless you have some kind of magic bullet you are not going to be able to but lets look at the logic.
Say we have a page of Widgets (brand) and they come in 7 sizes. When the range is fully in stock all of the brand/size pages will be identical to the brand page, apart from the title & description. So it would make sense to canonicalise back to the brand. Even when sizes started to run out, all of the sizes will be on the brand page. So size is a subset of the brand page.
Similar but not the same for colour. If colour is a tag then every colour sorted page will be on the brand page. So really they are the same page - just a slimmer selection. Now I accept that the brand page will contain all colours as it did all sizes but the similarity is so great - 95 % of the content being the same apart from the colour, that it makes sense to call them the same.
So for me Canonicalisation would be the way to go but it's just not possible as there are too many of them.
Noindex
The upside of noindex is that it is generally easier to put the noindex tag on the page as there is no URL to tag. The downside is that the page is then not indexed in Google so you lose a little juice - I would argue by the way that the chances of being found in Google for a size page is extremely slim, less than 2% of visits came from size pages before we junked them and most of those were from a newsletter so reality is <1% not worth bothering about You could leave off the nofollow so that Google crawls through all of the links on the pages - the better option.
Considering your problem and having experience of a number of sites with the same problem Noindex is your solution.
I hope that helps
Kind Regards
Nigel - Carousel Projects.