I usually put the kayak on my roof upside down if I can. Getting a cockpit full of rain while it's on your roof can add a dangerous amount of weight. If it's upside down, then a cockpit cover probably won't make any difference.
As far as straps, put a single twist between the anchor point and where the strap makes contact with the kayak. It will help. Make sure they're tight.
The Kayak Wing
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