Changing an award res: How to make sure the CSR doesn't screw it up?

I never would have thought to ask this question a year or two ago, but given the inexperience of some CSRs, the complicated challenges of working with SHARES, and the many instances of reservation screw-ups these days, I feel that I should. I've searched and found a few glimmers of advice but none completely on point, so I thought this might merit a thread. Mods, if not, I understand if you move it.

Anyway, I need to change an award reservation involving SFO-HGK-BKK-Vientiane so that the last (TG) leg goes to Chiang Rai instead of Vientiane. The first leg is SQ F (with the others on TG in J), so I'm especially paranoid about a CSR messing it up and perhaps even losing the reservation. FWIW, the seat is for six months from now and the BKK-CEI award seats are available.

I know that if I reach an obviously incompetent or unhelpful CSR I should simply politely end the call and try again. But sometimes such problems are not so obvious, especially if they involve systemic shortcomings.

So...any advice on how to best make sure that the change takes place as it should? Should I keep the CSR on the line until I see the change online? Is it necessary for the (revised) online reservation to indicate a ticket number? If not, how do I make sure that the ticket has changed, and not just the reservation? Should the change be nearly instantaneous on the SQ and TG sites? (I expect not.) If not, how long before it becomes apparent? Anything else to bear in mind?

What complicates this a bit more is that there are actually two reservations/tickets/accounts involved here, with identical itineraries and changes. One for me (using my miles) and the other for my wife (using hers).

Thanks for any advice!