Hi @Paolo Scamardella, nothing to be sorry about as you were very detailed with your current situation and gives everyone some insight into some of the options you've already done. I had kinda been in a similar situation as you a while back.
The home equity loan would be a 2nd mortgage and secured by the home tapping into some of the equity. This would most likely be a cheaper option and you'd be able to keep the home. The biggest thing is if you'd be able to remove your ex from the loan.
The cash out refinance is another option, and seems like you have a good idea on it.
Depending on where you live, will determine how big of a crash there may be (but timing is hard to tell on when it will/can happen). Some markets won't be as bad as others, but there is still a huge housing demand and little supply which makes it a little less predictable. Inflation is rising, rates are increasing and bumping some buyers out of the market, & forcing some owners to reconsider their living situations, especially if their income/job hasn't been keeping up with the costs. It is something to consider with potential risks, depending on your location.
One option you can consider is if your loan is assumable, you can most likely assume the loan and remove her from it. This is if the divorce is finalized, and (only) both parties are on the note. You can possibly speak with the lenders you spoke with before to double check if your existing loan is open to it. You could potentially do that then the home equity loan in order to pay her off.
If y'all sell, depending on how long you lived there can avoid paying capital gains taxes if you lived there 2 of the last five years. I think speaking with the lenders again to see. This can depend on what you mainly want to do.