You need to talk to your local gaffer supply/film production supply. Rosco makes a variety of gels and scrims to do exactly that, and they’re made to be near hot halogen lights.

How to diffuse light from ledat home

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Soraa makes a specialized bulb with a magnet and sell interchangable snap-on lenses that offer different types of diffusion, although they seem to only offer 2 sizes of bulb (including the MR16) and seem to be about 10x the cost per bulb ($25-26, plus $5-6 per diffuser) of ones with fixed / built-in flood ratings ($3 - $4).

How to diffuse light from ledwithout a diffuser

E7 combines the lighting comfort of LED+LENS™ technology with a robust, yet elegant industrial housing. This way, you can illuminate sports halls and high production halls with maximum visual comfort and high efficiency. All luminaires are impact resistant (IK08) and ballproof (DIN 18032-3).  E7 is available as a light line or as an individual luminaire.

OR Try this- High-temp spray paint, flat white. Make a cardboard template and start by spraying just a small circular area in the center of the existing bulb glass. If there is still too much light, make the template hole bigger and spray again.

Diffuser foil forLEDlights

E4 and E7: in-line luminaires are interchangeable, and additional headpieces must be placed at the start and end of the line.

How to diffuse LEDstrip DIY

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How to diffuse light from ledceiling

The specific luminous flux reflects the relationship between luminous flux and power consumption. Just as with fluorescents, a distinction must be made between the light source’s specific luminous flux (LED component, measured at 25° or 85°C junction temperature and with a standard control current) and that of a luminaire, including driver and optics.

How tosoftenLEDlights

Basically, you can replace the bulbs and look for a flood rating in degrees. 100bulbs.com says this for MR16 bulbs (YMMV):

I've ended up purchasing these recessed can trims with a diffusing lens. They're not as diffusive as I'd ideally like but it's better than before.

A retro-fit diffuser that fits with your make and model of housing/trim will be difficult to find (maybe impossible). Try different (lower lumen, different color) bulbs.

Our new home is almost entirely lit by MR16 - GU5.3 LED downlights that are too harsh for my taste. Snap-on solutions for the fixture don't seem to exist so I researched the bulb route.

It is also possible to connect luminaires together for in-line mounting, whereby the luminaires are mechanically and electrically connected.

I find the light to be too harsh and would like to have a way to diffuse it. Is there some sort of a diffusing lens I can install on top of the lights to make them pleasant to the eyes? Or should I just install a different lamp type if I want that effect?

Silk is known to soften lighting, but it's expensive & attaching it to the cans would be problematic. IMHO. I don't like the harshness of LED bulbs either. I replace them. There are various options with bulbs, such as "warm white" "daylight" "5000K"