I think what we need is an excuse for Amlach to not appear at the Council, and for Sauron to be reasonably sure he will not appear.
We have established that the gathering at Estolad is a regular event, so the default would be for Amlach to go there. And since he has a concern that he wants to bring up with others at this meeting, he has a strong motivation to attend.
So...what would keep him away? Yes, being made captive and guarded by orcs would do the trick, certainly. But is there any other 'emergency' we (ie, Sauron) could invent to keep him away? Travelling in Middle-earth takes time. If Sauron can verify that Amlach has gone back to whatever settlement he is from to *deal with contrived emergency*, then he can be fairly certain to not be interrupted while he is masquerading as Amlach.
Sauron could certainly intend to kill Amlach or replace him more permanently...but fake!Amlach's plan fails. No decision to attack the Elves is made. Hador unites the people to join Fingon, and Bereg takes the dissenters out of Beleriand, but fake!Amlach does not garner followers/support. So, at that point, Sauron likely abandons his plans and gives it up as a lost cause - these Men were not as easily swayed as he had hoped.
I have to imagine that real!Amlach has spoken somewhat disparagingly about the young men who have gone off with elf-lords prior to this. So, joining Hador and Fingon is still something he would be resistant to - he's not part of the newly-united House of Hador. But...he does want to join the fight against Morgoth, so he needs to find another willing elf-lord to join with. 'Why Maedhros?' is a question we need to answer, as up until now, there would be no reason to suspect that Amlach knows anything about Maedhros. What he and Maedhros have in common is the 'personal' nature of the grudge against Angband...so how will Amlach come to know that?