We are now at a stage where we'd like to apply for a green card for one of the founders. It seems that this is very difficult to do given that the requirements state that the position for the green card must be opened to all US citizens and the fact that the current holder is a co-founder, there's not a true intent to hire someone else, which is true.
Has anyone had any experience going this approach with a co-founder and their green card?
There's a special green-card category for investors, that might fit for your co-founder. Check the EB-5 visa. You should discuss this with an immigration lawyer, of course.
Obviously claiming that your position is open to US citizens when it is not is a fraud and may backfire in a DOL audit or even after the GC has been granted. Lying in immigration proceedings is a valid justification for administrative cancellation of the proceedings, including naturalization. You don't want to be deported 20 years after you have finished your naturalization just because a disgruntled ex-employee blew the whistle on you.
Get a good immigration attorney to walk you through the whole process and cover all your options.