Build another house on the property

Even if we sacrifice the garage, we would also have to tear down the garden shed so that one can access the rear property.

Unfortunately, your municipality is not yet ready to publish the development plans online. If there is none, development according to §34 of the Building Code should be possible, but not like in your plan, because this would open up a third row, which is usually not approved. In addition, the existing building is really very unfavorably positioned to use the existing access. However, you have three options to get access through the neighboring properties if the neighbors cooperate. My favorite is with a construction easement (green) over parcel 306:
[ATTACH alt="Lageplan.png" type="full"]46336[/ATTACH]