I liked the ability to set weapon proficiency but the rest of the monastery stuff was just filler. Replace it with a Tellius style base menu instead and whilst I'm on the topic of Tellius bring back bonus exp, ledges, the dawn brigade and siege defence maps. You can easily set the goals through a base menu with characters getting WEXP at the end of the chapter.
Reduce the load times, I swear I've not seen loading times like that since the Sega Saturn. Cut back on the graphics if you need to but that load time needs to come down. I found myself using divine pulse or turning the game off instead of retreating as I didn't want to sit through the loading screens.
Ditch the Avatar, we've had 3 Western games with it now and it's clear as day that you can't have a character that everyone can project themselves onto and and be a well-established character in the lore. Tell the story through the eyes of the lords and have an off-screen advisors like FE7 Mark if you really want to make the player feel integrated into the game. By having no Avatar the main Lord(s) can keep screen time and drive the plot. It would also remove an OP character from gameplay.
The deployment slots were poor compared to the units you could have effectively forcing the player to have less than a dozen favourites and a cast of bench warmers.
The routes are too similar from what I've seen so far although it's far better than Fates' shenanigans! Cut back on the number of playable routes and make it possible to save when they occur.
Edit: If I may dream for a moment I'd like to see the characters stop fighting themselves and instead become commanders and leave the actual fighting to more powerful, modern and expendable units which can be replenished for money based on how many resources you have/can capture. You could even take it into three dimensions with air units and naval units. Each character could do better with some of these units and worse with others.