The Thule Passage bike rack part # TH910XT that you referenced has been confirmed as a fit for your 1990 Ford Crown Vic LTD so it would do a great job to carry her/your bike.
Since you plan on carrying womens or alternative framed bikes without horizontal top tubes you may also be interested in purchasing a Swagman Easy-Out Women's and Alternative Frame Bike Adapter # 64005 to provide a horizontal top tube on your bikes to provide an attachment point. I attached a review video for this... view full answer...
How deep is it? It is hard to tell from the picture. You may be able to use some emery cloth and take care of it unless it is too deep. Then you would want to go ahead and replace the axle. Even though spindles are available by themselves you would need special equipment and experience to weld on a new one so that it is straight. Replacing the axle is the safe bet.
I have included a link to the axles we carry to the right. view full answer...
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