Wow Jersey. I did not need a COE permit for my pond, but (possibly) would for the biggee I plan for the future...we'll see.
I work in the enviro. field and have a few thoughts, similar to Svoberts'.
Navigability is a wide-open question. Have you had anyone (or done it yourself) research the average year-round flow on this stream? If it is really as small as you claim, you might consider doing this research and doing the calculations to determine how much "flow" you would be affecting. On top of this, obtain satellite photos and/or topo maps of the area, to prove no wetlands are involved. NRCS office can certify this part of the claim.
Now...here's where I always begin, if possible, in any permitting process. Go for the exemption. Don't ask for one, but in a nicely worded business letter, state your claim for exemption, and why it's valid.
Put this all together (keep a copy) and send it to the director of your regional office of the ACOE, not to the gal you originally spoke to. This director will put it with whomever needs to review it. Keep your original meeting with this gal out of it.
Put the ball in their court. This will make them provide a certifiable reason...chapter and section...as to why your exemption is not valid, if this is the case. No one person in any governmental body has authority to deny anything just because of their position. They must have a defensible reason.
They may, in fact, be able to deny your permit. However, in doing so, they must point to the section of code that invalidates your claim. You might have to have a lawyer actually read the section they reference to decipher if it's valid...but that's later.
Remember, these people have no incentive to quickly do anything...they just have to get it right even if it takes forever. I would add a section to the letter similar to "...barring timely response from ACoE, this project is scheduled to commence on XX/01/2006...". Give them plenty of time to respond...3-6 months or so. Send it certified and then at least you can show you interpreted the law one way, and gave them the chance to prove you wrong.
Long winded...but it's the gubment we're talking about.