Yes, your cylinders are indeed different from the everyday vertical cylinders that one sees. They are specifically designed for use in a specific horizontal position. Replacing them with vertical cylinders will not be good for your short-term or long-term health.
So the question is why you cannot get your original cylinders filled? Is it because they haven't been recertified? Rusted out or otherwise damaged? (Note that there is an exemption from the OPD requirement for certain older cylinders, namely, those manufactured before Oct. 1998, but these cylinders must have a label attached to explain the exemption.)
Lynn