,
the deviation from the development plan is not particularly large in your case, yet you apparently need to go the route of obtaining neighbor approval. The federal states handle this differently, and sometimes the practice depends on the respective building authority.
In NRW you could achieve the deviation through a so-called waiver building encumbrance - usually without neighbor approval. This basically works in such a way that you secure the additionally required area to the west of the building window by a waiver of an equally large area within the building window, thus only causing an individual shift of your building window without having to set up/change the entire development plan anew. The size of your usable building window then remains the same, so you consequently gain no additional building area.
Since in BW there is generally a synonymous handling of building encumbrance entries (some federal states don’t even have the construct "building encumbrance"), in my opinion this route without neighbor approval would also be possible in BW.
Clarify details with your architect/surveyor and building authority; you may then also not be able to submit a building application via the simplified procedure.
But as said, these are only a few square meters by which the building window would need to be adjusted and, due to the plot layout, this can be justified in my view.
Best regards
Dirk Grafe