I know it is a bit niche, but in v12 you could edit in some text editor once saved *.oll file (layout file) and re-arrange taskbar buttons like you want. So the next time you open this layout with multiple Listers they will be restored in exactly the same order as before.
But in v13 this trick does not work anymore, and even worse - the positions of restored buttons on Windows taskbar (i.e. windows order) is random from session to session.
It is just my Windows 10 being outdated and cannot handle something or you gutted that hidden feature along with the v13 development?
TL;DR: Something has changed in DOpus v13, i suppose it's something related to windows rendering or to the moment when windows pops on the screen. Perhaps it was a positive enhancement, but with one weird side effects.
Funny thing, if you edit file like i described previously (i.e. to forcibly sort buttons/windows on taskbar in a way you need them) AND replace "<wp " with "< " (without quotes i.e. remove WP argument from the file)... then everything will work as in v12, but with tiny windows opened in the corner that you will need to expand to normal size.
Also these tiny windows will be opened almost instantly, while without editing *.oll file they will be opened with a noticeable delay even though i have pretty beefy PC.
So i think random re-arrange on taskbar is related to how fast these windows can populate content initially, perhaps even before showing up on display.
So in the end i "fixed" taskbar sorting for myself with another hack, but the result is not very convenient. Well i guess it is better than nothing...
While i tested it, i noticed that on my PC 5-6 windows can be opened without any problems and in a correct order, but 6-10-13 is where the randomness begins to roll... Maybe his PC is just really slow or loaded with junk, so his own limit is 2 windows.
If you want to re-position taskbar buttons (lets just talk in a simple terms without Z-orders etc) then you just cut whole blocks between <lister></lister> in v12 or <lister virtual_desktop></lister> in v13 and paste it below or above similar block. The first block is the left button on the taskbar. And the last block is the rightest button, so you just move blocks like taskbar buttons.
You may want to open that Layout in DOpus before editing and compare it with these text blocks to get a better understanding.
To see what and where you re-position look for the first <pathstring> occurrence in these blocks - it will show you a folder path in the Lister.
That is all you want to do for v12 as it just saves positions incorrectly in these *.oll but it can open them correctly without additional editing.
To restore positions in v13 (assuming you have re-position problem, for me it only happens with 6+ windows stored in *.oll/Layout file) you need to replace every occurrence of (note: there is a space at the end of the line)
<wp
with
<
It will shrink all the windows and put them in the top-left desktop corner, but they will be correctly positioned on the Windows taskbar.
That's it. Not very hard, just unneeded/unwanted operation.