This discussion neglects the beam angle of the bulb in the fixture. These can vary from about 15 degrees to around 50 degrees. Additionally, tilting a Gimbel fixture does not necessarily cut off light as the beam is a three-dimensional paraboloid for which the math is much more complex than this simplistic tangent formula. The guidelines here will put you in the ballpark however. Unfortunately many "lighting experts" don't really know lighting. RPI (Rennselaer Polytechnic) has a lighting division with good information on line for those interested. I attended their one-day course prior to designing our own lighting for a kitchen renovation. The course was very helpful.

You can pull down the spot and fill it with a good quality filler (painters would use one they mix themselves) then let it set & sand. Repeat if necessary.

We removed 6 recessed spots from our breakfast room ceiling and replaced them with one central pendant light and it was the best thing ever! The lighting was always harsh even with trying all sorts of different bulbs and a dimmer but now it's transformed. We put off doing it for years as we thought it would be a major job and require re-plastering the ceiling but it was all done in less than 2 days. Our electrician did the wiring changes which didn't take him long and then the decorator patched the holes left by the recessed spots and used filler to blend them in. A coat of paint to the entire ceiling and you cannot see at all where the old lights were.

I agree that floor lights and/ or carefully positioned pendant lights will give a softer light for a bedroom. If you do decide to use downlights, some tips: Consider directional ones so you can point them at walls for a softer wash of light (and crucially away from your eyes in the bed). If you choose downlights with integrated lamps, make sure you get warm white ones - often the description says 'warm white' when the rating is 3000k - which is actually quite white/ cold for a bedroom. This might be useful: https://absoluteprojectmanagement.com/lighting-with-downlights/