It's been my experience that the less someone is willing to pay you for your work, the less they value it. Then every detail becomes subject to scrutiny on the invoice.
If you're good at what you do, and you can prove it, you'll eventually find jobs that pay you what you're worth. It just takes more effort to find them.
And of course, standing firm on your rates helps. You won't get all the gigs, but you probably don't want the headaches that would come with them.
Keep in mind that the negotiation on rate is a glimpse into how future negotiations will go. Contracting is all about negotiations. (Deadlines, feature requests, etc.)
The employer is looking to keep costs down. You're looking to eat. But neither of you should come away feeling cheated. Don't charge more than you're worth, and don't accept less.
If that's true, you need to start a consultancy with those "people with years more experience " as your subcontractors. You charge $40-50/hr for their time and pass through $25-40/hr to them. You both win.
Alternately, give a known quality associate a discount rate in order to get a firmer opinion of their work ethic.
At least while starting out, I'd emphasize quality over quantity. Alternately, go in as a team, and see how much slack needs to be picked up.