Is there a Yagi FM antenna small enough to be mounted flat on a vehicle roof for a low profile? And would it work when mounted flat (horizontal) instead of vertical?

I work for an engineering company that has designed and manufactured a product that can override FM radio (with regulators permission).

It is used by ambulance drivers in the Middle East and Asia to send emergency messages to surrounding traffic. For example the ambulance driver can say "Ambulance approaching, move out of the way" and every car with an FM radio will hear the message up to 200 meters from the ambulance.

Our company has chosen a small vehicle mounted antenna that is omnidirectional but I would like to offer customers the option to use a directional yagi.
Sometimes omnidirectional range will extend too far to the sides of the Ambulance which may not be ideal certain situations like when driving on a very wide highway.

Ideally we would use a Log periodic Yagi with 87.5 108.0MHz (Wide-bandwidth), 7 dBd gain, 50 Ohm impedance.

But these can be 2.7m Long x 1.68m Wide, 30kg and would look crazy mounted flat on a car roof.