If I were starting out right now I'd consider joining the AI and get really active in the chapter meetings. Take notes when there's a speaker and just generally work towards establishing a reputation. You don't want to be a leach or come across as an opportunist but you do want to show that you're serious about your career progression. Someone there will likely take notice and it will increase your exposure to whatever opportunities there are out there.
The other thing is that when you do get an assignment you will come out ahead in the long run by providing excellent quality and service regardless if you're happy with the fee or not. It's the same thing: you're looking to build a reputation for solving the more difficult appraisal problems, including assignments that other appraisers are actively avoiding because they don't pay as well as the simple assignments. Those difficult assignments will not be profitable on the basis of the fee, but doing right by them will be valuable in cultivating your professional reputation.
Lastly, appraisers are notorious as a group for their anti-social and anti-authoritarian tendencies. Most of us want to work alone because we don't work well with others. And sure, it takes a thick skin and a healthy dose of ego to stand firm when you need to stand firm. But you don't need to take it out on the clerks who work for the AMC or some reviewer because for them its mostly just business. Not personal. It never pays to lose your frame when you're interacting with your clients.