F1 income on I-864? (split)

[Mattew 0]

My wife is a US Citizen and we filed my I-130 & I-485 together. But I did not file I-131 & I-765, because I do not need to go outside of US nor look for job before getting my Green Card. I am a PhD student (F-1 Visa) with financial support (regular payment) from the university but I am not authorized to work in the US. My wife is a student without salary. As far as two lawyers told me, I used my salary in the form I-864 and we did not have any joint sponsor. But yesterday I received a RFE that asks me to submit evidence that the household member on Form I-864 (me) was authorized to work in the US (by work visa or employment authorization)!!!! I am not sure what should I do now…

There are several options:

1) Submitting another I-864 from my wife without mentioning my salary and using a joint sponsor on another I-864.

2) Only explaining that I am not authorized to work in the US (without filing a new I-864 from my wife) and using a joint sponsor on another I-864.

3) Filing I-765 and getting work permission and then using my salary!!

4) …

Also, if I use multiple joint sponsors (like 2-3), does it have a better impression?

Also do you think it is a good idea to submit I-131 & I-765 at the same time with answering this RIE although I do not have plan to go outside of US nor look for job before getting my Green Card?