How can I begin to gain credibility within the scientific community without a degree? I'm working on a fairly extensive multidisciplinary research project - something a bit outside the purview of what would even be difficult for a respected field researcher to publish.

That being said, I am quite aware of my own biases, and I am double and triple checking my objectivity on a regular basis.

However - without a degree, I've found it extremely difficult to get anybody to simply review the work. The immediate response is to totally shut down.

What are some good steps to take? Even if it takes some time, I'm fine with that.

I just need to gain enough credibility to simply get a few reviews.
I suggest that you read some papers related to what you are working on to see how your work compares. Try to develop a writing style that somewhat matches what you read. 

Then, if you think your work is ready, submit it to a journal, such as the ones you've been reading. You will get some feedback. If the work clearly doesn't measure up, the feedback will be quick. But if it is more or less appropriate, you will get, after a while, some detailed comments on the work, and perhaps how you might improve it. 

But the path to credibility runs through publications. The degree itself is less important other than to help an editor make a quick judgement.