I love your question! Well, I really like the no shoes policy. (I have to mop the floor continuously because I live in a dusty area though, but it is totally worth it)

You are definitely gonna have to go for the strong and memorable strategy, but make it fun and amicable.

Remember that very few people are used to this so we are the ones going against culture and common sense, but that's OK, there's definitely a way to make people understand and remember.

**Be explicit and official about it:**   
Organize a party and add the "no-shoe" term in the title of the invitation, make it sort of the main theme. Because you are not asking for a favor, this is official.

> You are invited to my No-shoe movie night (party, drunk night, sleepover, whatevsies)

People remember the purpose of a space, the first element/step was setting the narrative (invitation cue), the second element/step is setting the scenario, the shoe basket is a nice start but you need to make it 3dimensional to have better results.

**So, play with spatial cues**   
- Trace a clear rounded or squared line on the floor that marks a noticeable frontier/border from side to side where shoes are allowed for them to remove them.   
- Slippers are a great option, but some people are germophobic/mysophobic and they would prefer seeing a basket of thick socks they can put on instead of slippers, the socks basket needs to have a note that say "freshly cleaned"   
- Add a place to sit next to the line delimiting the shoes-allowed area, so they can sit and go about the business of taking shoes off, putting slippers or socks on or whatever.

**Why?**   
Our minds set our behavior very much based on the place we are navigating, architects know this, in fact, that whole profession is pretty much based on this concept, the experience of the space. Even atheist people behave in a certain manner when visiting a catholic temple as tourists, and people who are usually very territorial about their personal space dare to surround themselves with a bunch of strangers at a dance floor on a night club.

You will also need to be amicably and sound sincere while saying something like "I don't care if your feet smell, everyone's feet smell" (you might regret this, but hey, you wanted people to take off their shoes)   
The shoebag/cover someone recommended is a nice alternative to avoid this.   

I personally prefer to mop the floor every time I have people visiting because I am a bit of a germophobe, and I'll defend that by saying I'm rather germoaware because I used to have problems with my feet when sharing shower and shoes with my brothers while growing up, I hated it, I love having my feet perfect, I obsess about it, I obsess about my girlfriends' feet too I guess. Second guessing the health of stranger's and friend's feet conditions and health disturbs my stomach. People who don't want to take their shoes off might be aware they have an infection, don't make them feel so awkward, street dust at sunny cities are germ free, you might prefer the dust.

And lastly, I wished this was not necessary but, make sure your place is extremely, super clean.   
There was a friend that shared my no-shoes policy but she had a hard time keeping it clean because she had kids and cats, getting surprise gunk or invisible sticky goo on one foot or sock is extremely disgusting, I won't be able to put my shoes on and infect them on the inside where it's marginally possible to clean.

If more people knew having healthy feet is not that hard at all, things would be easier for you.

Best of luck.