Since @jprspereira tagged me I will throw in my two cents. 
If your interested you can look into some of the Anki work I have posted in the forums that may help.
I have a small collection of tutorials that can get you started -
As well as a collection of decks -
→ [ Some Supplemental Material ]
The best example probably being my modified version of the 10k -
→ [ Complete 10k ]
Specifically in regards to your questions about a prebuilt IME, it can certainly be done. My decks include a script created by Viet [ WanaKana ] that works great for this.
Currently I have found the answer to the problems you have by using Kitsun.io instead of Anki. It gives an easier experience with a lot of prebuilt features that just makes the flashcard quality of life so much better for me. You could give that a shot as well if you like.