Did I transcribe 'Linschoten' correctly?

No, it should be Лінсхотэне or Лынсхотэне (the i sounds like Ukrainian и).

By the way, Dutch has "многа народу"; if you could do something with народ in your translation, that would be really nice, it would make it a better translation of Dutch when I link them.
Only if it doesn't make it a worse translation of the English sentence, of course. :)

Well, as far as I understand, Belarusian 'y' is a closer sound than Ukrainian 'и' (Bel. /ɨ/, Ukr. /ɪ/), so I'll leave it 'i'. I don't think I've seen a letter 'y' in Dutch placenames.

"Narodu" is somewhat more colloquial than "ludziej", but maybe it's OK...

"Mnoha" looks like a Russism for me. :o Though maybe it's worth adding, because we have no examples with 'mnoha' in Belarusian at all, and it's a rather widespread word.

Yandex returns 13'000 results for "прыйшло многа народу" and 42'000 results for "прыйшло шмат народу".

Oh, I found "много народу" in the dictionary. :) But just choose whatever sounds more natural, after all I don't know any Belarusian. :)

I've ended up adding both. ^^