I think I understand what you're describing; I have a couple of spaces like that in my house. And your under-the-roof storage area is very deep at the lowest extent, right? Much farther from front to back than it is up high.
If that's the case, one option would be to build extra-deep shelves for the lowest portions and use underbed storage totes in those shelves. You could slide them in and out like drawers and not lose anything at the wayback that way, use up all that volume. It's not too different from your current usage so it wouldn't be hard to adapt.
Since it's kind of an odd situation (but not that odd), you won't find any ready-made inexpensive solutions, just some solutions that you can adapt with a little extra effort. Since it's a unique situation any solution you come up with you're probably going to have to fix yourself. That said, it's easy to do. Your shelves can be as simple as full-depth plywood shelves with sufficiently high legs attached that the underbed totes can slide under. Here's where you can be very efficient, making the legs exactly high enough that the totes just fit under with no wasted height. Then you can add another shelf above that with another layer of totes, etc.
The legs don't have to be anything more sophisticated than pieces of 1x lumber. Cutting is easy if you don't have tools: take your measurements to the home center and usually the first couple of cuts are free, subsequent cuts have a nominal fee but it's still cheaper than buying a saw...unless you decide you like the result so much you want to do the entire attic bedroom all the way 'round, in which case more power to you.
You're giving up a lot of volume behind those dressers, you have the capacity to get it all back. I know you said you don't have a lot of money to dedicate to this project, but one cool thing about it is that since it goes up in a complete, single shelf, you can do one this week and stop. A full sheet of decent plywood is maybe $15, all the totes you need is another $25 (maybe), 1x lumber = $5-10.
Another $10 for hardware (almost optional) and you're looking at a total outlay of $60 for a single shelf. And there you stop. One layer of totes underneath, baskets full of clothes on top of this new, raised platform.
Save up for another couple of weeks. Build another shelf at exactly the size needed, probably a few inches shorter (front to back) than the first one. Totes, baskets, probably don't quite need as many baskets.
Save up for another couple of weeks. Repeat. Continue repeating until you have all the storage you want or you run out of vertical space, whichever comes first.
It goes together in stages and looks finished, or nearly so, at each stage so you can live with it as it is and not feel bad about how it looks. Always buy the same brand of totes so the appearance remains consistent. When all is said and done, it won't look like custom cabinetry but c'mon - it's an attic bedroom. How special should it look? And it will live well and use the space efficiently.
Good luck with it.
Handyman. Most of the shelving in my house I made myself to custom-fit the space where it is.