Unless your AA#7 powder charges are compressed (and I doubt they are...) I would question the theory that a slow gentle ram movement will produce a different cartridge OAL than a hard fast movement. 357 Sig brass is pretty tight in the neck, and also fairly uniform, so I doubt the seating speed can make any difference. The ram will come to the top of its stroke at the exact same position regardless of its speed, and I think the case mouth grip is way too tight to allow the bullet to "slide" further into the case.
Now with compressed loads of AA#9 powder, ram speed is VERY much a factor because you are compressing the powder and there is some springback in the compressed powder that can push the bullet back out of the case. I have found that a slow, deliberate ram movement should be done to initially compress the powder, followed by a 2nd bump at an equally slow speed. The fact that you have a single station press will complicate things, because the way I do it on my turret press is to seat the bullet with the slow double bump method, and then shift the turret and crimp the bullet only a couple of seconds later. You will probably have to seat 50 bullets, and then put in the crimp die ASAP, and be sure to measure the rounds to make sure the bullets have not backed out of the case before you apply the crimp. You will have to watch this like a hawk!! It almost might be worth it to get a Lee single stage press that comes with the reloading manual for about $30 if you don't already have the Lee manual.