The practice method you talk about is very similar to WaniKani’s joint website, KaniWani
Unlike what you describe, though, there aren’t multiple-choice options for you to choose from.
And the site also has some drawbacks. One of these is that it’s rather inconvenient when it comes to synonyms; for example, the word “woman” can be said in many different ways in Japanese, but you won’t necessarily know which word they’re specifically asking for.
I like the idea of practicing from English to Japanese too, since it’s what you do when speaking and writing (until you start thinking in Japanese, that is) but I don’t use it that much, personally, because KaniWani doesn’t have userscripts I consider crucial, in particular the auto-commit; the end of the enter key script. If a user script like that came out for KaniWani, though, I might end up actually using it.