OP, it doesn't hurt anything if you size the cases twice, might even decrease some more runout as the case position will be different the 2cnd sizing.
One thing to be aware of with SS cleaning is the case mouth gets peened. No biggy for plinker ammo and pistol but not ideal for precision rifle. So I trim .001" off and deburr inside and out or at least debur. I've been going two firings before I clean with SS because I'm lazy and don't want to hassle with trimming every time, plus I don't want my brass getting shorter and shorter. One other thing...I apply NECO dry case neck lube inside the necks with a Qtip right before I seat the bullet because the cases are so clean there is a lot more drag compared to a fired uncleaned cases.
If you happen to have a Ultrasonic cleaner you can run the cases first for 5 minutes to loosen up the carbon, then it only takes 45 min to finish cleaning the SS way. I got lazy and quit doing that too, LOL.
Oh, since I have my brass weight sorted into 50 round bins I only clean 50 at a time. So I grab 3 cases, swish them in the dirty water to get the pins out, then rinse at the sink which I'm standing in front of, deposit in a bowl lined with a towel, blow dry with wife's hair dryer and let sit overnight.