So what happens when you can't find a solution to your problem and hit the edges of current research even specialists cannot buckle?

I say, "you're going to need to pay a team of PhDs to work on this to maybe get a solution, eventually, or change your approach. Here's why: [evidence]"

I've never worked with or for anyone who wanted to hire the team of PhDs.

this is often a sign that the design/solution you've chosen is an unfruitful path.

know when to cut your losses and try something different.