I don’t understand your distinction, mutual intelligibility does not discount a tongue from being a language, and discounting dialects from the accent <-> language continuum seems overly logocentric. I agree that dialects like Scouse, Strine, Geordie are not distinct languages; I also think that a rest-of-The-world English speaker would struggle to understand a speaker going full-on with the vernacular.
The trouble with finding equivalent meanings between words with similar spellings/pronunciation is that you’ll conclude English and Dutch are the same language (or Danish/Norwegian/Swedish)
I've lived in Norway for the last 32 years and from my English vantage point Norwegian and Danish are definitely dialects of the same language. Swedish is the one that has made the most progress to becoming a separate language because of the large amount of vocabulary that is not shared with the other two but it is still not really distinct. All three have essentially the same grammar and syntax. I can converse with educated, well spoken, Swedes because the pronunciation is very similar to Norwegian even though spelling, vocabulary, and usage often differ. On the other hand I struggle with Trøndersk which no one claims is a separate language from Norwegian, and Danish is almost impossible in conversation because the pronunciation is so different from Norwegian but reading it is very easy.
These three languages are much more similar than Dutch and English.
I agree with the principles of what you say but I also agree with the other reply to you. It is definitely a continuum and we can only impose artificial boundaries to it; what is mutually intelligible to one speaker may not be to another. However, from my experience of the accents of the Atlantic Archipelago (owning to my political bias here!), I don't think Scots is more different to RP than Scouse or southern Hiberno-English, perhaps with the exception of some very isolated communities.
The trouble with finding equivalent meanings between words with similar spellings/pronunciation is that you’ll conclude English and Dutch are the same language (or Danish/Norwegian/Swedish)