Your making to much work for yourself. Your going to have a difficult time dialing in what the proper strike temp should be by doing partial additions. Winter, Spring , Summer, or Fall, I always preheated my mash cooler 10 min. with full bore hot tap water. Dump it and added my strike water which was 3 degrees hotter than the software said. Get all the strike water in and shoot for 152 degrees with the software and see what you actually get. If you end up with at 149 or 154, your still in the sweet spot for a decient beer. You can adjust the temp of the mash tun in most software to get closer to the proper strike temp. Just be consistant with how you approach this. Next mash you will know better how to adjust the strike water. After a couple of batches, you will be confident about hitting your mash temp.
Target getting all the water in first, then stir in the grain
Dial your new equipment in!
Gary