In my experience, you can't work direct for HUD unless you have the ability to cover a region for them - I can't and don't want to do that, especially for HUD.
On the other hand, getting paid HUD prices is easier. I simply demand them. That's what I charge, take it or leave it. I realize that getting my pricing may not be that successful for everyone - I cover a notoriously hard to cover territory. Almost every client I've ever dealt with understands that fact and is willing to play ball right from the first phone conversation. Even if you don't have the same situation where you are, don't underestimate the power of negotiation when it comes to pricing.
Regardless of insurer, HUD pricing is always a good benchmark to use - Either start higher and negotiate down, or maybe have a maximum discount in mind and shoot for that. If you're getting $20/CY, it's because the company you're working with negotiated your pricing and you agreed to it. As a business owner, take charge of your own company, decide what you need to get paid, and go find clients that will pay your rates, they're out there.
While I'm new to this, I second the pricing and taking charge. If they choose to not to accept my bid because of my rates, that's on them. For private customers (residential and business) I charge minimum $32CY when you base it on my cost per load. If you start at my initial pricing, it's closer to $48CY if you're within a 20 mile radius, and between 20-30 mile radius it's bout $64CY. The harder the job, stairs, and distance affects these prices too.
Don't let anyone but you decide what you're worth when it comes to pricing. I agreed to remove a washer and dryer this past Saturday for free, because it was working units. I could have sold the set for $150 instead of charging $120 to pick it up. When I got there, the seal on the dryer door was hanging down, and the back of the washer was literally taped on. I told the guy I couldn't take it because normally I charge $120 for what I was doing for free. I left there without anything, even scrap. I know my worth, and while it took time out of my day to go to the job, I'm worth more than the crap they were giving me. In the guy's defense, he's not the one who set the whole deal up, and I felt bad because you could see I upset him and caused him to stutter. I just feel like the person who initially set it up figured if I got there and it didn't work, I'd take it anyway. It's the first job I've walked off from after showing up to, and I've been doing in home junk removal for probably about 5 years and have been burnt more than once by a customer lying. I'm just not doing that anymore. I quit my job to work for myself full time, and I know my worth. Know your worth too, and either they use you or don't. You'll find plenty of other jobs to do with or without them, at the prices you're asking.