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Hey there! I just had a look in your campaign and from spot checking it does seem that the drop in ranking is being reported accurately by using Rank Tracker and also doing some manual searches as well.
As far as to what impact of changing the theme and and removing indexing, I can't say for certain what impact this would have so I'll let an SEO expert answer those questions 
I know the Crawl Test reports are cached for about 48 hours so there is a chance that the CSV will look identical to the previous one for that reason.
With that in mind, I'd recommend waiting another day or two before requesting a new Crawl Test or just waiting until your next weekly campaign update, if that is sooner
Great answer Dirk! Thanks for helping out!
Something else I noticed is that the site is coming back with quite a few errors when I ran it through a 3rd party tool, W3C Markup Validation Service and it also was checking the page as XHTML 1.0 Strict which looks to be common in other cases of 406 I've seen.