What he said is a good idea.
As a Glenn Miller fan--don't drill that record just to play it on a cheap replica--when (not if) you upgrade to an antique machine, you won't want to have the good records slopping around on the turntable.
Take the platter off, and then take a piece of 100-grit sandpaper and sand the spindle down to where it will fit records. Use your record with the least damaged spindle hole in it to measure until it just fits.
Now--for making your gramophone play. Your sister is very kind, and is probably a lovely person, but the Indian replica machines are not particularly good for actually listening to classic 78s. Set your needle angle at 60 degrees trailing along the surface of the record. Seal all joints in the tonearm with axle grease or Vaseline. Replace the needle after each record, and, since the replica soundboxes are not particularly compliant (flexibility in the needle bar, just like in a modern stereo) you will want to break in the tip of each new needle in the runout groove of the record you are about to play.
Adjust the motor to 78rpm. The speed dial may not be accurate...test it by putting a piece of paper under the platter and take a watch with a second hand and count off 20 revolutions in 15 seconds. This is a speed of 80 rpm suitable for Columbia records of the pre-1925 era. Back it down a hint. Your 78s should sound decent. Early Victor recordings (batwing or patents labels, pre 1925) can vary in speed. Some run around 75, others closer to 80.
Now make sure the horn doesn't fall off because it doesn't have a rivet securing it to the soldered-tin elbow.
Put on a favorite record, write your sister and thank her, and get to the Yankee Trader and ask if any collectors have a phonograph to get rid of! A horn machine can be had with a bit of patience or a Wanted ad, but I'd personally suggest a console or upright Victrola--they are big and durable, the lid keeps the dust off, and they're awesome. I have had one since 2016 (a Victrola XIV, built from 1912 to 1923ish--mine is a 1914 model) and it's great.
Other people will love the Victrola Orthophonics, introduced to play electrically recorded discs after 1925--like Glenn Miller and other swing and hot jazz classics. Try the elegant Granada 4-40, a petite 4-3 Consolette, or the mighty Credenza. Should you want the warm rich sound of vacuum tubes, look round for a Victor Radio Electrola, like the RE-45. 1920s radios are really neat and some can have amazing sound on AM.
Good luck, and hope you can either make your little phonograph work, or end up trying one of the classic machines of yesteryear. Many of us keep our antiques on active service and use them everyday. I know I do--that's how I listen to music.
