Yes, CG films are famous for “slightly altered” trade-names … the Shrek series was full of 'em.
However, all of those uses, being “parodies,” were cleared by the studio’s legal department.
And that’s really what you should do here. As your game nears the point where you know all the logos that you intend to use, engage the services of a qualified intellectual-property attorney to review the material, to point you to the proper places from which to obtain permissions (if and as they are, in his/her opinion, required), and to give you a letter on-letterhead which states that in his/her opinion all of the necessary steps have been taken and the uses are legitimate.
Now you have “done Due Diligence,” and you can prove it. You looked for "i"s and dotted them all; you looked for and crossed every “t.” You dutifully “erred on the side of caution.” If someone comes after you and says that you infringed, you have a credible defense. And, in my book, that’s well worth the several thousand dollars it might take. It’s a fully-deductible expense of the project, of course. It’s quite handy to be able to say (knowing that the clock is now running): “Hey, Hank, come take a look at this and tell me what you think …” Hank knows.
You’re engaged in a commercial venture. It is, I think, prudent to "ask someone who really knows, and to pay him or her for their professional expertise.
No, I’m not a lawyer. But I’ve engaged, and thus befriended, several of them over the years. One fellow’s way of putting it was: “I’m the one who finds out where the rocks might be, ahead of time.” Good point.