To an unobservant reader, that is me, it sounded like the answer was already in your post.
1. You said you cannot or will not, in near future, publish enough papers that will qualify you for EB2 NIW GC self-petition.
2. You are not tenured track. So your current employer, which is an academic institution, will not file for GC. And you are not going to be tenured in near future.

It sounds like, to be in an Employment Based Green Card sponsorship program, you may need another employer.

** That was a plain vanilla suggestion. Personally, it sounds like NIW EB2 is tough nut to crack sheerly because the burden of proof on you is heavy. It sounds like a philosophical question, at this point. I will share my personal situation and you may extrapolate. I was a mediocre student. I did not do academically well. I applied for US student visa because it was a fad in my workplace in Nepal. Similar to lottery, I suppose, I got lucky and completed my plain vanilla masters and then chose the desi IT company route for work and GC and have been leading my mediocre life running the same rat race. When I was a Gas Station attendant, I never thought it would be pretty much easy to get an IT job and get a GC. Unaware, I was a beneficiary of the same loophole Alexia Fernandez Campbell talks about in The Atlantic, in her December 6th article from last year. Anyway, when I reflect back, I see it was my desire to live a mediocre life. But the one that had a US permanent residency in it. You on the other hand, my friend, are in the cusp of brilliance and academic breakthrough. Where you are touching the lives of dozens, if not hundreds, every day. You are the unflinching Professor that has faith in her student. The one that will change lives of people. The one that will change the course of history, dare I say!

HI,
I think when you talk about EB2 GC, you are actually talking about EB1 which is extra-ordinary category to file GC. In that case, you need to prove that you have extra-ordinary talents in the related field, that is your academic field with enough of publications and citation. Actually, EB1 is for researchers, PhDs, Professors , Artist who can prove their talents (EB1-is the category most of the Nepali Artists file GC and get through easily in 5-6 months, even being filed in Nepal. You know some of them, right ?). For EB1, you do not need any sponsorship, you can file indivisually.
So, now EB2 and EB3 are other two category where you can file through company sponsorship. Based on your experience, I think you can easily qualify for EB2. For any Non-profit organization like University and Hospitals, they can file EB2 for you and the benefits that you do not have to fight for the quota system. Now, the issue is current H1B bill of 130K seems to be problematic and if its passed through senate, it will be tough to get GC through H1B. Since you are already in H1B, its extension seems to be uncertain at current situation.

So what option do you have ? of course file GC through sponsorship if your current H1B status is still valid or you have TPS with EAD. There are lots of consultancy in the market who can file GC for you.

@Neerman: the University already told me they will not file EB2 for me. My option now is to do self filing of EB-1 (I often get mixed up with EB1 and EB2) or either through consultancies. Do you have any suggestions of good consultancies?
@Kalidasbhaisab: thanks for sharing your experience.

HI, post your resume online and watch the show. You will get 100s of calls from Desi consultancy with promises. So, choose the one that has success track records. There are some Nepali consultancies too. Do some research and call them directly, hope something works out for you.
Good Luck,

Sarkozy, by saying "very few journal articles" how many do you mean? If you think you don't have enough credentials for EB2 then don't even think about EB1. I have seen somebody with just one first author and one third author paper getting EB2-NIW (Those articles were in journals with 2 or 3 impact factors). You probably know that EB2-NIW can be self-petitioned too as is EB1A. Here is my suggestion :- if you think your publications are not enough for EB2-NIW, then write to journals to volunteer as a reviewer. Big journals won't give you a chance, but you can go with smaller journals. Trust me it works and in 2/3 months you will have reviewed at least 4/5 manuskripts. It will help a lot in your case.
Hope that helps

If you have option to file EB1 yourself why not go for it while waiting/pursuing other options as they come? Except for $$ to be spent is there any drawback of self filing EB1? You know the worst that can happen ..which is same as not doing anything.