Backgrounds wise... while I can see the attraction in having hand drawn backgrounds that match the style of the artwork, I'm also inclined to think it would probably be a mistake to go down that route. Not because it would look terrible, not at all - but because it would take so much work (and time and budget) to create the sheer number of backgrounds that will be needed to portray the world our characters live in. And.. we have such human feeling characters, who live in what's pretty much the real world. Why not take advantage of the fact it exists (and that you more or less live in the same neighborhood as them)? Focus resources on unique signature pieces like Jayda's exhibition artwork, or additional sprite variations - and relish the opportunity and flexibility that you have in more-or-less living where the characters live.
Would the story work nicely if they could visit a particular location that doesn't already have a background, but they'll only visit it once? No problem! A photo may take mere moments out of your day to take a snap which will set the scene perfectly.
All that said, I do also favour lightly filtering the images, as Katawa Shoujo did; I think it takes the edge off the character/background contrast nicely. While Who Framed Roger Rabbit? in particular was amazing, that was all about toon characters in our real world; our darlings are very real characters in a real world, so I don't think we need so much contrast in style between the two.
And I should say that I'm really happy to have found LoveSick Darlings at this relatively early stage in its development; I completely agree about how much better a tale is when characters exist and interact with each other, and continue to do so even if the protagonist is pursuing a particular character's "route" (which I think has really let some of the "big name" visual novels down, too). And so I'm delighted to be able to help out behind the scenes doing time-consuming things like hunting down stray typos, which will allow Dimitri all the more time to truly develop the story and its characters. Meaning that in the end, we all hopefully get to read a better story, sooner (because let's be honest, it can't arrive soon enough).