We do have E visa but not sure if allowed to travel on that.I fail to see why people with travel plans in January and beyond are still depending on OCI which is known to be a drawn out process. Some of us who were thinking of e-VISA for pre-planned travel in October to mid December landed in a fix with the unexpected visa suspension. And we were compelled to use OCI as the only option left. But that crisis is nearing an end except for those having family emergencies.
If your travel in January is very important, apply for entry visa. Otherwise get OCI in hand and then plan travel.
Your chances of getting OCI before Jan 2 is non-zero but not very promising. If processing continues at the present speed, you may get it around end of December but its likely to slow down further. Add to that delays due to Christmas/New Year holidays, and it looks risky.