"Hard to imagine a lawyer being hired who doesn't believe in the Constitution who makes strict Constitutional arguments before the SC."
There's where you're wrong. There are plenty of lawyers who do just that. How many on the left argued for states' rights, then federalism, when it came to gay marriage, and on abortion can turn on a dime and argue that Roe is right and incorporation's the greatest?
You're right. You have heard the adage about the professor asked whether he taught that the earth was flat or that the earth was round, and he replied that he could teach it either way the administration wanted. So it be with the lawyers!