Hi John,
Although I do expect you will find the water may be coming in at the transmission cover as Bob suggested, a friend had a similar issue that drenched more than the rug. When his Healey restoration was completed, one thing they did not do was to put the seal under the blocking plates used to close the openings used for brake and clutch in rt. hand drive cars. Although I can’t remember if they exist, but if there are heater and/or plenum drain tubes, I would look to make sure they are open and extends to the outside.
Ray (64BJ8P1)