Never known someone so tied up is semantics.
Me too, and I am renewing both of them next month in the UK where, on the current passport application/renewal form, they do request that not only do you need to provide the concurrent passport information, but you must also submit it when renewing either of them. Since I am renewing both at the same time as a walk-in at one of their offices (time pressured), I won't need to send anything away. I will be providing letters from my employment agency to support these renewals, same as the original request and on subsequent renewals.
Note that when I renewed them the last time, I did each of them one month apart at the old Trendy location in Bangkok. They only required a full (all-page) photocopy of the other concurrent passport included with each application rather than sending it to the UK, and they took less than two weeks for each renewal.