I know what you mean. With Morgan I use a mounting block but out on a ride sometimes you do need to get off for whatever reason!
At this point my girth is tight (as I have done it up after getting on at the mounting block and strolling around a little so if I have to get off then the girth is still tight.
When I need to mount I first make sure that Morgan is lower than me (ie check the ground level and use it to your advantage by pointing the horse in the right direction), I then lower the stirrup by about 3 or 4 holes so that I don't have to do gymnastics to get my foot in and am in a better position to be able to hop from my ground leg. At this point I do not hold the saddle at all. I use a hunk of mane and neck if I need to and then push from my ground foot up and over. This way the saddle does not move at all. It is near on impossible for me to mount from the ground with my riding length stirrup. So once up I just then shorten that one side.
Does that help at all?
Obviously your horse has to learn to stand still when mounted and also be able to tolerate you pulling a little on the mane/withers but I have to say Morgan is happy for me to do this but is not happy at all if I grab or drag on the saddle while mounting. Of course you are going to have trouble doing this with a western saddle!!!!!!