What if you use a coax with two shields, one shield for chassis ground
which is the coax connection and the outer shield for earth/ground?
Yes, there could be a ground loop but the nearest ground to a strike/
antenna is probably the best protection

You'll still need to deal with RF currents flowing on the outside of the
coax (and also potentially between inner and outer shields).

A good transient suppression scheme at the entry point deals with the
overvoltages from lightning, power lines falling on your antenna, etc.

The challenge is in protecting a sensitive receiver front end, while not
introducing other problems: if the receiver burns out at 1Volt, a clamp
at 300V isn't going to save the front end, although it will keep the
radio from catching on fire. A diode clamp to the supply rails or
similar will save the front end, but will almost certainly result in IMD
issues with strong input signals. Sometimes, the front end just has to
be the sacrificial "fuse", so you want to make sure that it's a cheap &
replaceable part that suffers.