Do you have someone in your area who knows how to handle Macaws, there are many ways in handling Macaws, I too do not like towels but sometimes you have to do what is best for the Macaw and your safty. You can also try a hand held perch to see if they will step up onto it,then place them into a carrier,
If you or someone you know, knows how to restraint the Macaw, this is sometimes better as you have full control of the Macaw and a lot safer for you.
You have to look at this, this way, If something is wrong with your Macaw, whatever it takes to get them to an Aviary Vet is most important here. It is not normal for a Macaw or any bird to rock and swing non-stop.
It could be that no knows how to handle them and they will do strange things to get attn.
How long has your Macaw been in their cage without interaction from you or previous owner. Joe