In my experience, which as you know is coming up closer to 40 years worth than I want to admit, the percentage of plans that allow active employees to make transfers to even qualified plans not sponsored by the employer is very, very low. I'm not going to go so far as to say it is zero, although I have never personally seen or sponsored one that did. But the OP is an active employee; if the plan is considered an current employer plan the OP is still subject to the rules of the plan document and the distribution rules contained therein. Everything he has posted so far suggests that it is considered a current employer plan. If he finds it's not, okay then; maybe there is a loophole somewhere. But if it is, there does not "have to be" a way around the regulations just because he is in need of money just now.
A case in point. My employer completely closed one plan more than fifteen years ago. No contributions have been made to that plan by anyone since 2001. Employees who participated in that plan are grandfathered; they will not lose that benefit. However, they still can only take distributions according to the rules of the plan. It is not a free checking account that they can draw on at any time, simply because contributions are no longer being made. It is still a qualified plan and subject to qualified plan regulations.
And, less than a month ago, I was involved in a case just like the OP's - an employee wanted to take a withdrawal that is not allowed by the regs and insisted it was "his money"; we had no right to withhold it from him. Except that we do have both the right and the duty to adhere to both the IRS regs and the plan rules, which as you should know if you don't are set in stone once they are established. Even if the employer once had some choice in the matter, once the choice they made is set into the plan document they cannot deviate from that choice without changing the plan document. Which is a very big deal to do.