All vehicles will be different on battery vs running, as that voltage increases by two volts. You are correct there are many charges to the flat response, which is why most of not all solutions, other than JimmyTs will never sound great. You must get a dsp that cab compensate for the changes. The Audisonl has this built in, so you end up with flat response. Prior to post eq changes it also supports.
For 250, you can get this
c-dsp product and with some documented magic, you can theoretically achieve the same. This product is not processing at the same high sample rate, but should suffice.
I will post what the curve looks like that comes from the head unit. I can assure you, with the Audison, the overall sound quality is very high with the head unit. I have captured SMAART fft traces comparing the signal output of source device against the measured output of the speakers.
I look forward to learning a less expensive way. That would be a holy grail.
Robert