You can also actually file off the front left corner of the 2015 logic board where it doesn't fit (with a fine tooth file, nothing crazy) because the 2015 for wtf reason used a smaller radius curve on that corner vs. the other, and the 2016-17 board has the same radius curve on both sides. There's nothing but silicon on that corner and I've made successful replacements of 2015 batteries using pulled bottom cases from 2016-17 this way. Just have to round off the very corner just a bit, and everything is otherwise exactly interchangeable. Also you'll end up with more battery life using the 2017 given that it has a higher mAh rating than did the 2015 battery. I'll always recommend a pulled, tested OEM bottom case vs. a 3p battery because I've never been able to find a third party battery for the a1534 that isn't crap.
As you said none of this works in Sonoma and up, but... The step you are missing to remove the account before rebooting are (after deleting and running all the other commands because you won't have permissions otherwise): sudo rm /var/db/dslocal/nodes/default/users/shortnameofaccount.plist Then reboot
On the 13 inch, you can swap logics freely between 2009 and 2010 (both Core2Duo, but there are internal changes, bus speed, faster processors that make this an upgrade, and you can swap in a faster processor logic), but no others. You can swap freely between early and late 2011 (again for faster processors and Apple-undocumented design flaw revisions). The 2012 13”, at the least, has a different SATA cable than the previous years, and a couple of connections on the logic that are transposed but within the tolerances of the cables on the 2011; and I have not experimented with this swap out, self. On the 15”, you lose that freely swapping ability between 2009 and 2010 because the changes in board design to use the i5 vs the Core2Duo moved other things around on the board. When in doubt, you can lookup the board replacement instructions here for the different years and compare the pictures and notes.