What I meant was that combined with moving the panel to the right with @Lhc_fl component. Studying the code in the component I linked, you might be able to put the hamburger menu back between the search and profile. If I understand your request and issue with the current workaround made by Lhc_fl.
As it already uses code to move the menu it might have details in the code as an example to modify to be able achieve the desired effect your looking for.
On mobile your screenshot is in the desired position your looking for on Desktop mode.
Someone with the experience might be able to extract the code used in mobile as well and apply that to desktop. Via either or both studying inspect element on desktop while loading site in mobile view.
For width there is a new component to change site width that maybe of interest to explore.