Is sanding the only way to remove semi-gloss paint from a high-gloss surface?

Pretty much. You will never get it all off though. The problem isn't the sheen, you can't apply latex paint over oil based paint. Sand what you can and make sure that the glossy finish is roughed up. Go to a real paint store (not Lowes or Home Depot because they don't even carry interior oil based paint) and buy a quality oil based paint and "liquid sander". A real paint store will know what it is and can probably give you more insight as to how to apply it and finish prepping the surface. Multiple coats of paint may be necessary to smooth surface. Over time it will cure and harden giving you the best adhesion possible at this point.