As long as you're using tap water, there's no need to let it sit unless you've got really sensitive fauna, and that's mostly regarding very large temperature differences. My advice is fill a bucket in the tub and dump it in straightaway, then treat with Prime for the entire tank volume and walk away. While I understand wanting to be cautious, it sounds like you're putting too much thought into this.
My routine, with larger water changes, is to hook up a hose to the bathroom sink, run it to the tanks, and let it run. I turn up the hot water a bit to minimize temperature difference, but it's an unnecessary step IMO. While I wait for one to fill, I treat with Prime for the whole tank. Then I use the shutoff valve I have installed at the end of the hose and move the hose to the next tank. The hose has a faucet adapter at one end and a PVC "U-turn" at the other end to hang over the edge of a tank, with a "T" and two HOB intake plastic mesh screens at the ends of the T to spread out the flow. I use the same hose to drain to the tub, btw.
*Edit* I edited the super-high-resolution photo to be a little clearer and add the shutoff valve and PVC faucet piece that keeps the hose from kinking.
Last edited by kevmo911; 12-07-2015 at 12:16 AM.
Reason: modified the pretty pic