No what I do is take the left rein and get her to reach her head around and after she stops spinning I take the rein up to the saddle(while her head is still turned to me) and them get on. That sometimes works but I still have the problem of her jumping around when I get In the saddle and I have I hold her back because she wants to go before I'm ready.
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I treat horses that don't stand to mount like getting on colts for the first time.
I start out like you with the left rein brought in so the horse is looking at me and if he does make a move it's in a tight circle. I stick my toes in the stirrup and stand in the stirrup, If he moves I still have the left rein and it will be a very tight circle. When he stops moving I get down, release the rein and pet on him. I repeat this several times until I can stand in the stirrup with out him moving his feet.(on a colt I do it on the right side as well, but that is up to you and be prepared for the right side to be worse and be careful as he may have never been mounted on the right.)
After that you can start completely getting on, be very aware of yourself when swinging your leg over and setting yourself down in the saddle. You plop down they want to leave instead of staying planted. Again keep that left rein, when he moves keep him bent and when he stops his feet, release the rein and just sit relaxed on him. If goes to leave again, do it again.
Keep doing it until he understands that he is to stand until you ask him to move off. It will take some time and you may want to devote sessions just to work on mounting, when you he does good and makes progress put him away. Let it sink in.
One word of caution, and I know that everyone does things differently, but please do not back a horse as soon as you get on, I have seen some wrecks due to backing a horse after getting on. (rearing and flipping over backwards) I am not saying that all horses will or yours will but it is something to be aware of.