A few thoughts:
Are they just not going to do have the audit done for the years it was a large plan? That is a compliance issue I couldn't ignore. Either do it or move on.
How many years to review? You know of issues going back to 2011. Same theory as above applies. You can't ignore known compliance issues. And these are pretty bad. A 35 day average for a large plan is a BIG deal to the DOL. You need to go back to 2011 and fix it.
You can apply the 7 day safe harbor for the small plan years, but not the large. Unless you extraordinarily complex payroll system, 6 days isn't going to fly for a large plan. This is one of those "the rules are the rules" situations. 35 days 15th of the month following are non starters. An auditor will probably apply 2 days but sometimes a few more in rare cases, if reasonable.
Here is what it comes down to to me: Don't make the clients problems your problems. They have serious compliance issues. Those issues need to be fixed properly. You are a professional. You know how to fix those issues properly. Don't create problems for yourself by not doing it right just because you want the business. It isn't worth it. Hopefully the client will realize that you are looking out for them and do the right thing.