General aviation pilot reported on initial climb noticed the oil filler door flopping around. They notified the Tower; which then gave landing instructions; but during the approach they were high and fast; and after touching down they went off the end of the runway.

Narrative

On initial climb out (300 - 400') I noticed the oil filler door flopping around. I notified tower which offered either a closed pattern or tear drop. Alarmed by the movement of the oil filler door - I was concerned it would detach and come through the windscreen - I opted for the tear drop. I rushed it and rolled out too high and close to make a landing. I requested a tear drop at the other end of the runway - winds were calm. I went further out before turning; but still rushed it and was somewhat high for the approach. I elected to continue and landed long and hot. The end lights on the runway were inoperative and I thought I might be able to stop. Wrong. I went off the end into the grass and stopped after ~100'. I taxied back onto the hard surface; and to the ramp.Upon inspection; the bolts holding the filler door were worn and just barely settling in the over-centered position. Not enough; apparently. One bolt departed the plane.Replacement bolts are on request. I have asked an A&P to inspect the landing gear for evidence of problems. The same A&P advises that Gorilla tape will secure the door (and remaining bolt) until a permanent fix can be made.I have scheduled a night proficiency flight with an instructor.