I've previously said that it didn't really matter when you submitted your manuscripts--and in one sense, that's still true. You can submit whenever you want, but you may not get read in a timely manner. If you want a reasonably fast reply, July and August might not be the best time to submit to LDS publishers, especially the smaller ones.
For example, I'm still accepting submissions and people are still sending them, but those that arrived after the middle of July are still sitting unopened on my desk. And they will continue to sit there until after the convention.
Maybe this is not an issue in the bigger houses, where you have one job description per employee. But in the smaller houses (defined as fewer than 6 employees), everyone is working on last minute convention activities. This is the time we temporarily stop looking for new stuff and concentrate on selling what we have.
So, if you've submitted to any LDS publisher in the past 30 days and haven't gotten a reply, wait at least until September 1st before giving them a nudge.