My DD is a little younger at 2.7 yrs but we have always used the mat for time out. It can be anywhere we are (if ata friends we use a mat there)
I give her fair warning that she will go on the mat if she keeps being naughty and I guess because we have always used that method she knows its a big thing to be sent to the mat. She is a very sensitive child though so if she is ever put on there it results in a massive meltdown and a mass of sobbing "sorry mum's" which breaks my heart but you have to stick to something.
We plan when that stops working or as she gets older removing privledges or favoured items for a period of time. We already will say to her if she is disrespecting her toys etc that if she continues they will go in the bin. A couple of times I have actually grabbed a plastic bag and appeared to be chucking said toy out, which again results in a massive meltdown and the toy is then removed from play for a week or so when it magically reappears unnoticed
It's hard coming up with something that works. We don't do smacking and have always taught DD that if someone smacks her its wrong and she should tell me. So it wouldnt make sense for us. Hope you find something that works for you