Curious what type of balancing machine your are using? I'm not really sure how an exhaust system can create a vibration at the exact same freq as the blade rate/first order vibration unless the balance machine is not filtering the input.
Sorry in advance if this is too much nerd detail...
Let's say the exhaust system has a normal mode, aka resonant frequency, at 97 Hz. (Actually, it has many many such modes at all sorts of different frequencies)
Any excitation source in the system with 97 Hz content will set the exhaust ringing like a tuning fork - resonance.
The source could be anything from a rotating imbalance, combustion forces, valvetrain forces, flicking the the pipe with your fingernail, or who knows what else, the exhaust system doesn't care.
When excited at a resonant frequency, the response of a vibrating system is amplified.
The exhaust is not creating it's own excitation source, it is simply amplifying the excitation it receives.
So if the engine is run at 5800 rpm, the imbalance will be generating a 1st order excitation at 97Hz, which will excite the 97Hz exhaust system resonance and increase the 1st-order vibration measurement.
In order to electronically filter out the effect of any resonance, you would have to increase or decrease the engine speed such that the entire width of the band-pass filter was sufficiently separated from the resonant frequency. That distance depends on how much damping there is in the mode of interest and the shape of the filter used.
Although, if there is a
stable resonance at the balancing speed, it would just boost your signal to noise ratio. Have to be careful though because modes move around with temperature and such.