Thank you both, Tom and John. I've consulted an old dictionary as well (1861), and it simply does not include "hoogedelgestreng". It does include "weledelgestreng" and notes there is no translation for it, advising to use "Sir", with the possibility of adding "Esquire" as suffix.

Indeed "Most Honoured Sir" or perhaps "Honourable Sir" would be best. "Worship" or "Worshipful" might be useable as well, as I gather it has judicial connotations. Yes, it's laying it on thick, but this is also the impression in Dutch, to a modern reader anyway.

(The letter is from 1816, so no war anymore.)