Inshot burners = small and basically crude jet engines when it comes to the sound they produce, especially when directed down a round tube.
Tubular heat exchangers made of as light of material as possible to get the best efficiency, but yet heavy enough to not fail within warranty period.
Complaints of cool/cold air blowing out of supplies on start-up. Solution: Fire burners at max. at start-up with blower delayed and/or running slowly to pre-warm air.
Complaints of noise at start-up. Help from anyone at the co. or the engineer that spec'd it with a solution: That's just the way it is. Sucks to be you that you're the lowest person on the food chain and now have to come up with an after-the-fact solution. The manufacturer sold their "best thing since sliced bread" to the engineers that specified the equipment but didn't understand it's non-documented characteristics, but it looked good on paper. And then the famous "you must've installed it incorrectly".
Real world is to know what you're dealing with and how to guarantee a solution. IE: What frequency is the offending noise. How is it being transmitted. What are the documented ways of attenuating this frequency. How to "fit" this now known and documented solution into the situation you're dealing with.
Aaron probably is not going to be much help because they are only responsible for the equipment and nothing beyond the base or duct connections from it. What they MAY be able to supply you, if they're willing to share the information or not, is the frequency that their engineers and designers "know" is being produced by the burner/heat exchanger arrangement. If you can't get this info from them then find someone in the audio world that can come measure the "noise" and tell you what frequency(s) is/are the problem. Make sure the teachers are there at the time so they can go "THAT'S IT!" Each frequency has a way of being attenuated. It might be as simple as lining the duct work with an acoustical liner. It may require the installation of a section of "muffler" duct work with sound trapping built into it.
Fixing things that others have decided is not their problem because they can hide behind the veil of "We only design, build or specify it" is what makes our job not only frustrating, but it also gives us the advantage of being able to brag about skills that the "others" will never appreciate or understand.
Use the biggest hammer you like, pounding a square peg into a round hole does not equal a proper fit.
Aaon's are pretty noisy when operating normally but I have experienced the "jet engine" noise you described. Normally this is caused by the baffles in the heat exchanger falling down because of corroded or broken screws. All you need to do is remove the heat exchanger and reinstall the baffles with stainless steel screws. You might need a little bit of fire rated caulk just in case the gaskets are in bad shape. But since you said the unit has been noisy since start-up, I am not positive this is your culprit.