You have the skill, you have the resume which can absorbe eye ball, these are great!
Some agent do check reference at first to be sure the candidate they talk with is worth their time.
If I were you, I will give name and phone number out once I decide to give them the information, otherwise it is useless for my refence data.
What you said: "but I don't think I pass the behavior questions." is a problem all of us should know before we start send out our resume.
As one of my student told me: Proffessor Tu, you should tell your students: if they don't know how to answer the behavir interview questions, that means they are not ready for the interview.
My suggestion is: Prepare the behavir interview questions. Be rady for the interview. keep looking.
I listed the 89 behavir interview questions prepare by 梅影 before in my website, you can get it.
Thanks!