Maybe some engineers with graduate degrees will chime in but I think you’re overthinking this. If you like Lafayette and are doing well why transfer? It’s an excellent school. The grass isn’t always greener on the other side of the fence. It kind of sounds like you’re having buyer’s remorse about Lafayette.
As long as your grades and scores are good combined with good experience you can succeed anywhere. Many top graduate programs take students from much lower rated schools than Lafayette. Are you planning to contract in ROTC and serve full-time or reserves? You can get plenty of good engineering experience in the service.
I doubt CMU has changed much in the 30 years I graduated from Pitt but my friends that went to CMU worked their tails off. The kids that go there live, eat, and breath CS/tech. Engineering is great too but not sure that ChemE is their strength though. That said, it is one of the best CS schools in the world and the opportunities there are amazing. You have access to things that most other schools can’t provide.
If you are doing well at Lafayette, staying there might give you the best chance. Your standing with professors and performance are the key factors along with certain tests to get into grad school or research. You are taking a bit of a chance transferring into whole other programs, and you are not going to get a break if your grades go down. I would imagine you have better opportunities to get to know your professors and get recommendations and even placements from them, with Lafayette being a small school Not as easy to make a splash at CMU , Cornell, GT. You have to start over as no kid on the block. Not saying, you can’t do it but if you are going for the odds, my opinion is that they are better where you are
your decision in transferring should be based more on fit, being challenged, not finding right social groups, rather than class rank, which is not all that important for grad schools, where gpa, course rigor, test scores are more important. It’s possible that Lafayette could be considered a positive for b-school as they’ll get a lot of applications from the CMUs and Cornells of the world. For b-school, your work experience will be important, so focus on accomplishments, leadership roles, managing people if you can.