As a visitor rather than local I'd say Carsaig would be a better launch point than Tayvallich as if Jura is your target it's a bit of a drag down the loch from Tayvallich to get out into the sound... it's further down the loch than the crossing distance Carsaig-Jura.
From casual observation I'd have thought like Jambo that a sensibly parked car to the south edge of the Carsaig green near where the bushes start wouldn't attract complaint.
The main advantage of starting from Tayvallich would be the excellent slip and pontoon facility with mains water so you could get launched and tied to the pontoon then take the car/trailer to where you'd arranged to park. Finally before you set off do not pass the village café by... we nearly lived in there the 4wks we've spent in Tayvallich?
As Jeff mentions Castle Sween holiday park is another option as it gets you a start much nearer the mouth of Loch Sween and there's a café there too for stoking up before you leave. We've had several cottages from them over the years and the booking office people have always been very helpful.
Its looking like i've a week at Crinan the week before Jura so will be able to suss out Carsaig a bit better. I've been there before i got into boating so never really paid any attention to launching parking etc. Thanks for the suggestions.