I don’t think any reputable service would cash it as a third-party check signed over to someone it isn’t made out to.
If you are in CheckSystems because an old account was overdrawn and went into collections, you can probably go to the original bank branch involved and talk to one of the branch officers. Tell them you have a problem that they can help you solve, and they have a problem you can help them solve. In other words, you have a mututal interest in seeing the check cashed. Offer to open a savings account (can’t be overdrawn) if they will let you deposit the government check as the opening deposit, less whatever you owe them. They get to recover funds they otherwise may have to write off. You get a savings account, and can withdraw funds once the check clears and you have repaid the bank, and while it will take a month or more, you will eventually get updated in CheckSystems as having had an issue, but having made it right. That’s a much better situation than you have now, and you will, after CheckSystems updates their listing, be able to open a checking account in a bank where you did not have the original problem. The bank where you had the original overdraft won’t take anything more than the risk free savings account for 2 to 3 years. But other banks not involved in the original problem will.
Of course, all this relies on the government check being big enough to cover the original debt and you being able to part with the needed cash to pay if off. If that’s not the case, then you are stuck with the outrageous fees check cashing services charge, and you have to risk walking out of there with a fist full of cash in your pocket.