Just apply a degree of pragmatism.
The time to discuss manual flying is probably at the briefing stage before descent, not the moment you disconnect the autopilot.
Agree a method for doing this - provided it's briefed and not explicitly forbidden by your ops manual, there are many ways to skin a cat. I usually brief that I'd like PM to make the changes immediately on hearing the instruction from ATC, and I'll verify it from the FMA / PFD. Consider doing it FD off so you don't have to keep asking PM to fiddle with vertical speeds / FPA angles etc, just headings / altitudes.
Ultimately if you're in a particularly busy environment as you describe, perhaps it's not the best time for manual flying?