Most of the extensions apply for due dates on or after April 1. The S corp election for a calendar year corp was March 16. So it appears that at this point the only way to do a late election is to request a late election from IRS. Not sure how much this costs.
In doing some further checking, I think they will qualify for an extension because S corp elections are included in Rev. Proc. 2018-58, which is incorporated into the current extenssions IRS will grant
You can definitely file a late S election with the extended return using Rev Proc …i dont know the number off the top of my head…but…..the instructions for the 2553 have all the details. You will have to file the return on paper…..we have done this many times with no problems.