In that specific instance, you're assuming way too much precision in terms of how shipping and commerce actually happened. The deadline would be more like "sometime in late summer I'll drop off your trade goods."

In terms of record keeping, you can convert among calendars just like we can among time zones today, with a chart or almanac or something similar to that. But payments, interest due, taxes owed and the like would be handled on the local calendar's basis.

(Interestingly, speaking of calendars in my age of specialty, officers were traditionally paid by the lunar month, resulting in 13 "paychecks" a year.)

I unfortunately can't answer that question, but I am curious as to the source of the 1752 adoption of the Gregorian calendar

Shipping was more of a "when it gets there" rather than a specific date.

When George Washington would order something from Europe he would always write "at your earliest convenience" to his shipping merchant Robert Cary. Cary would respond "Expect it during X month or X season.

This doesn't answer your question specifically but it gives you some insight in to notions of time. Railroads and railroad timetables really standardized our notions of precise time in the late 19th century.