Accidentally contributed to pretax 401K

Dear Community,

 

I accidentally contributed to pre-tax 401K from one pay check. In my memory, I didn't do it. It is some issue with the portal. All my 401K contributions have been after tax Roth so far and I want to keep it the same way even now.

As soon as I noticed that this mistake has happened I notified my employer and the broker and they said that it will be fixed but I saw it is not fixed yet and now they are saying that they can't fix it. 

Do I have any option to resolve this?

I was thinking about the following option to my rescue:
Context: This year I have changed my employer. I was contributing to 401 K even with my previous employer. So my new (current) employer relies on me to tell when my contributions have reached the limit. I am thinking to use this as leverage with the following plan. 
Plan: I will let my this year's contributions go over the limit (new employer's pretax + new employer's Roth + previous employer's Roth). I will do this by contributing more in after tax Roth with the new employer. I will do it such that   new employer's Roth + previous employer's Roth meets the limit. But when new employer's pretax is considered I will be over limit. So when it will come to fixing the over limit, I will withdraw the money from pre-tax section?
My questions:

  1. What do you think about this plan? Is this feasible?
  2. If yes, what are the pros and cons of this?
  3. If I let the money remain in Pre-tax, how does it impact me?