Firstly, sorry to hear of your wife's ill health.
Car and Classic auctions are a different kettle of fish, I've know a few to sell successfully there. One winning buyer, only one person to come round and take the car away. Okay, there's a commission to pay if sold, but if you don't achieve your reserve, just pull the plug - nothing ventured, nothing gained and it's not cost you a penny.
That really is a stunning TR6 - I only wish I had a spare garage space for it!