What is the I-140 category? If NIW, you don't need school HR's permission, and you cannot do I-140 premium. If it is university sponsored PERM based I-140 or EB1B I-140, you can do I-140 premium if H1 6 years expiring in 60 days. If EB1b, I suggest you do I-140 premium, because you and your spouse may get GC based on your I-140 sooner than based on spouse's case.
If EB2, quick I-140 approval probabily won't make any difference to GC waiting time, and whether to do premium will be based on whether you want to extend H1 beyond 6 years? You can use EAD just fine without H1, and no need to worry about status problem with an approved I-140.