'Right Honourable' does have specific social connotations in English which, as you rightly suggest, would not sound quite right in a military setting.

I wonder if something along the lines of 'Most honoured sir" or 'Highly esteemed sir' might fit the bill, although not as flowery as Hoogedelstrenge.

strenge - 'stern' or 'severe' is hard to render in English as a term of address - 'Most honoured and worshipful sir'- perhaps?

That would seem to be laying it on quite thick. Don't they know there's a war on?