Speeding up does not work, that'll just put it in a higher orbit. My understanding of these issues is that introduced eccentricity gets you: if it takes the "inside corner" (is that the English word for binnenbocht/innenkurve?) around the earth, it could then then meet you on the other side where the orbits intersect. If it sped up (flying out of the corner, in this race analogy) and thereby took a longer way around, it'd rather be a danger to those immediately behind (with each orbit, progressively further back along the circular orbital path)
Disclaimer: this comes from playing a self-made orbital mechanics game, I have no training whatsoever let alone professional experience with this