Oh for Pete's sake. Tying to the bars has been done for years and years and years. I tie my bikes down at the bars to this day and have never a problem to date. (I've forgotten more miles towing bikes than most people will ever tow theirs in their lifetime.)
First, get long enough soft ties so that the ratchet on your straps will not hit the chrome or paint. Then loop the soft ties over the bars at the bend closest to the forks and you'll be fine.
On chrome (or stainless) bars I've never added anything to the soft ties for chafing - chrome is pretty tough stuff and it takes a lot more than a nylon strap to scratch it.
If you don't have a stand alone chock you can build a frame stop out of a couple of 2x4's, placing it under the frame so you can pull the bike down onto it. You won't have to collapse the forks as much and it'll add lots of stability to the strapped down bike.
And as previously said tie the rear of the bike to prevent side to side movement.