On a sport utility where you can spread the bars sufficiently apart you can get by with a short tray and no problem of clearance of the chainring. However, someone does make a front fork mount extender. The folks that use front fork mounts in vans have the same problem and I have seen these extenders use by them. Sorry I can't provide the manufacturer but someone certainly will if you keep asking.
I have always tried to avoid the bottom bracket tandem racks and currently use long tray that Yakima sells with a Yakima rack that clamps to the down tube, hence I leave both wheels on and the bike rides just fine on top of my Jeep Grand Cherokee. It has ridden thousands of mile up there and suffered no ill effects. Clearly if you go the downtube clamp route with both wheels on, you should be sure that the clamp mount is able to accomodate your down tube diameter. My old Santana Arriva does not have particularly large tubing, but if you are dealing with a newer fat tube you will have to get the mount that will fit it. I hope this helps.