So if you've read the above, and are still convinced it's worth the effort to bring her on board, then a new challenge begins. In many ways, this is a self-resolving challenge if you're prepared to stick to the following principle:
If you need to offer a salary that matches the day rate for a contractor to come on board, then the fit is wrong either for you, for the contractor, or more likely for both.
In other words, if the only way to bring her on board is to match her rate, and assuming that's a day rate that's higher than a consulting salary at her level, then save yourself the effort.
There are two main approaches to salary structures. That is if you've got a salary structure in place rather than paying what you can get away with / what it takes to get someone to join or stay. The more traditional one is to have salary bands for levels of consultant. A method being increasingly adopted is to recognise that you may have superstars at any level, and to pay them accordingly - the "10x coders get 10x pay" approach.
Regardless of which approach you take, you shouldn't break it for your contractor. First, it would run against your principles (hopefully). Second, even if it doesn't, and word gets out (which, believe me, it always does), you will create unnecessary friction amongst team members, unnecessary pressure on the new joiner, and unnecessary pressure on all your salaries to head north. All of these will make for a less happy, and higher churning, workplace.
Your consultant may need you to match that rate. It's not unreasonable to assume that she's at a place in her life where she needs it. If that's the case, then I would strongly suggest you continue your relationship as client / contractor rather than break your salary system.
However, if she doesn't have that immediate financial need, then you can start the last stage of discussion - namely why it may make sense for her to take a cut in terms of hourly rate for enhanced security, prospects, and a different way of working.