My suitcase recently bit the dust too, but it was a hard case. This reminded me that I need to go shopping for another! Anyway, I've found that, whilst the screen partition can be useful for keeping stuff in the mesh pockets, it can be annoying in that things don't always stay well slotted behind it. The things in the top half of the suitcase (that acts as the 'lid') usually spill out from the sides when I unzip the suitcase lying down (by virtue of lifting the lid).
So instead of putting things in the top half that are easy to slide about (due to the lack of straps to hold them down - why don't they put straps in both the top & bottom half?!), I instead use my packing cubes in the TOP half to hold things together. It sounds counterintuitive but, since it's the lid (& therefore needs to be able to flip up easily), I put lighter & sleeker items in the packing cubes in top half (I usually Kon Mari my clothes if they're tightly packed, otherwise rolling them helps to stop unravelling). I then wedge anything that needs to stay flat (like a jacket) between the packing cubes & the top lid. Anything that needs a little more wiggle room but doesn't like being completely strapped down (like a hat) goes on the opposite side of the packing cubes, next to the divider instead.
I then put all my bulky items in the bottom half, so that they can be strapped in, & will stuff smaller items into them (stuffing socks into knee-high boots, for example, helps them keep their shape but also makes a logical 'footwear' category in my packing space). I use the crevices between the items for flexible stuff that can fill different shapes easily (like belts) & anything delicate goes into the mesh pockets in the divider (underwear & jewellery, I'm looking at you - packed in little bags first though, so that they don't snag on the mesh).
If I'm just bringing the hardcase as a carry-on, I will also then keep anything that isn't essential to keep on me at all times (since that goes into a tiny crossbody) but that I may still need before I get to my destination, in a separate 'somewhat essential' purse. I'll load everything else up into the suitcase whilst it's still laying flat, THEN stand the suitcase up & slot the 'somewhat essentials' bag into the very top. That way, if I'm ever in a rush (or just want to add something in the airport but not have it with me in my aeroplane seat), I can easily slide my hand in to the half unzipped suitcase to get to it (without having to lay down the entire thing) - very useful in a constantly moving queue, like airport security!
It's also great because, once I get to my room, I'm usually exhausted regardless of the time. I can easily pull that somewhat essentials purse aside first (without fully unzipping) for any pressing matters needed right then & there - I'll pack my first night's pyjamas in it if I'm arriving at night, or a change of underwear & clothes if I still have some of the day to sightsee. TMI sorry lol but I can't stand wearing my flight clothes any longer than is necessary haha!
Then I lay my unzipped suitcase down for a bird's eye view of everything else - I may not unpack it all then & there, but it sure makes me feel organised to know I don't have to root through everything to find the now essential stuff for my first few hours at my destination (especially when I'm already starting to feel the jetlag, lol)!
This may not be that relevant if you're doing shorter haul flights only, but I hope that helps!