So let me get the snark out of the way first: as a former proud owner of a '59 Austin-Healey, my hat's off to you for taking a vintage roadster on a road trip.

That said, your challenge packing is the space you (don't) have. Do you have a trunk rack for extra gear?

I would think once you get two sleeping bags and a tent in an MGB trunk you're starting to push the limits.

First off: backpacking sleeping bags will pack much much tighter, and will also lighten the load in your wallet.

Second off: see above. You want to consider using backpacking gear rather than car camping gear, as item for item the backpacking stuff will be smaller/lighter.

Lastly: pack a membership in a good auto club with towing services! :)