I've never hacked an LGB engine, but the Aristo stuff I've abused has worked well using a method I devised... the scrap styrene from kitbashing gets placed into an empty Plasti-Weld jar. When its full, poor some fresh plastiweld over it. long term soaking will cause the styrene to melt. If you use just teh right amount of solvent you will get a putty-consistence. use this just as you would any other type of modeling putty. Because it is plastic, once the solvent dries out, you will get a plastic weld, which sands smooth just like the parts you were cementing together.
Now, the question is, would this solution work with LGB plastics? I can't answer that one for you.