Hm, Gumshoe will require a bit more work then.
Direct murder and murder mechanisms are both still possibities.
We know that gumshoe was dead the minute Phoenix opened the door to the room, because blood is present on his sprite and death was instantaneous. I find it unlikely (for now) that Gumshoe faked his death, only for Edgeworth to finish the job during his examination, so I will assume the murder happened before the door was opened. One possibility lies in the order of leaving the room; It is emphasized, and Phoenix declares he was the last to leave the room in red, but nowhere does it garuntee that no one entered the room since Phoenix had left it. Currently, the murderer role for Gumshoe is still generic, as they could have killed him by slipping away unnoticed... but given how you've dismissed my earlier solution, I doubt this will stand for long.
Mechanisms are possible, but I'd rather not dive into that rabbithole if I don't have to.
As for the adhesive solution, there are still ways for Larry to escape his position.
1. Lisa did come back with the solution for him, but Larry then took her back to the room and killed her, and then placed the adhesive back on himself in the meantime.
2. In the event that #1 is disproven, a there is a weaker approach that might still hold; Larry was not fully covered in the adhesive, as the red truth says it covered his SHOES, the FLOOR, and LARRY HIMSELF. The coverage on the floor clearly wasn't large enough to prevent Lisa or Edgeworth/Phoenix/Maya from going around it and getting to the solution eiher. I propose that Larry could have placed his jacket on the floor and taken off his shoes, letting him jump/walk over the small adhesive puddle to get to the storage room. He could then kill her, and place himself under the effects of the adhesive again.
However, the first solution brings up two contradictions I'd like to address;
1a. Like said in my previous theory, if Larry was the culprit he could have closed his eyes when walking to/from the hallway himself.
1b. If someone other than Larry entered or exited the hallway, he wouldn't have seen them. He was glued in place in a specific location, and was facing the door to Nanotech. (It's pretty surprising he got all the way there from their struggle by the door, but that distance combined with the context of the struggle serve as evidence that he would not have been facing the hallway at all.)