Dear B,
There is not an unofficial score report for the TOEFL, IELTS or PTE; that only applies to the GMAT. So, in looking at your options, I strongly encourage you contact HBS before making the determination between option b and c. You definitely don't want to do option a. Depending on HBS' stance and how strict the admissions office wants to be on receiving test scores by the deadline, you might be able to be considered in R2 with the understanding your new TOEFL will arrive before the decision is made. However, you will need to have that agreement from the admissions office--don't assume that will be the case. If HBS is willing, then you would write the letter/email explaining your previous (expired) TOEFL, instruction in English for your degree, and plans to retake the TOEFL (including test date). If HBS is not willing to accept your app in R2 due to the test scores not arriving, then you will have to move your application to R3.
Good luck,
Lisa