I know from personal experience that a good t can help you work through attachment and transference. However, your t has made it clear that she feels uncomfortable with the subject and avoided talking about it until she had to. She has been honest in admitting that she doesn't have the skills to help you in this area.

You have said that this issue is very important for you to resolve, and very painful. It then sounds like you need to go see a therapist who has knowledge and experience dealing with severe attachment and transference problems. It could be the male therapist your own therapist recommended, or it could be a different therapist that you find doing an online search. You can do an online search for a therapist near you, and in the search box, try adding the word "attachment." That way, you are more likely to find t's who specialize in that issue.

If you decide to see the male therapist your t recommended, don't assume that he is highly skilled with attachment and transference issues. Find out by asking him specifically how much knowledge and experience he has in this area. You do not want to start with a different therapist, only to find out that he isn't the right person for you either.

You are obviously emotionally attached to your current therapist, and don't want to stop seeing her. I get it and understand why. So why not seek out a new t with the skill and experience you need to work on attachment issues, and accept your current t's offer of keeping in touch via email during the process. If it doesn't work out with the new t, you can always go back to your current t. And if it does work out with the new t, and you get a better handle on your transference issues, you can still go back, right? So you would not be losing your t.

This is just my opinion though. You have to do what seems right for you.