If you go on the Scillonian ship, the 4 hours on Scilly does allow you enough time to get to Tresco to see the garden. When the ship arrives in St.Mary's, local boatmen will be waiting at the quay to ferry people over to Tresco. They charge about £9 for the trip which takes about 20 minutes. You also have to add £15 to get into the gardens. Should you go, I would not book the ship until you know that the weather is going to be good. Book on 01736 334220. Also note that for even more money, you can fly over from Land's End Airport.https://www.islesofscilly-travel.co.uk
You could not have chosen a more awkward London starting point for your journey west than Greenwich. You will have to negotiate London before you can start heading west. Two routes link London with Exeter. The northern one takes the M4 towards Bristol and then you join the M5 to head for Exeter. This route is 30 miles longer than the southerly one but is all on 3 lane each way motorways.
The southerly route leaves London on the M3 before heading off on the A303. This route practically passes Stonehenge - so you could throw that in as well - but on such a long journey, you would really not have time - unless you have an overnight stop en-route.
From Stonehenge (Amesbury) to Exeter you have a mixture of dual and single carriageway road.
From Exeter to Penzance, the northerly A30 route is the quickest.
http://www.theaa.com/route-planner/index.jsp#fromNode=0%7CGreenwich%7C%7C-0.007659%7C51.482577%7CtoNode=0%7CMousehole%7C%7C-5.539062%7C50.084245
In view of the long distance, you might like to take the train. That being so, you should pre-book a specific train at:> www.gwr.com
You may like to go by train (from London Paddington) as far as Plymouth & then rent a car or go all the way to Penzance. You should
also be aware that a sleeper train also operates the route = 'The Night Riviera' - but it is expensive.
https://www.gwr.com/your-journey/journey-information/on-board/night-riviera-sleeper
Check for engineering work on your chosen dates of travel with the Great Western Railway. (Sometimes they leave from London Waterloo when this happens).
The Eden Project is incredibly popular and queues can be bad around 10am. I would go and have a look at nearby Fowey and perhaps Charlestown first to perhaps arrive at Eden around 1.pm. https://www.edenproject.com