Yes, objective measurements should definitely be the priority here as that's what this project is all about, and the resources and careful methodology required for proper scientific listening tests would be immense, too much for one person to organise.
I don't think listening tests prior to measuring would have any undue effects on the objective tests though, while eliminating a major source of subjective expectation bias, and so giving listening impressions a bit more reliability. Measurement selection bias can be easily eliminated by deciding beforehand on a fixed set of measurements that are made on all speakers.
@amirm using a standardised template for measurement reviews would help here (as well as for DAC/amp reviews), so no measurement is assumed, or forgotten to be measured/posted as has happened in the past. I think Reference Audio Analyzer's 'Reports for Pros' does this standardised format approach well e.g.
here is their report for the LG G7 and
here is their HiFiMan HE-400i report, which have the same structure for all DAC/headphones reports. Of course, further measurements can be made if a particular feature/failure needs more investigation, but all equipment should be tested with the same initial suite of measurements.
This leaves interpretation bias, which as you say, can be ameliorated by being 100% transparent and presenting all raw measurement data publicly (again, the same goes for the DAC/amp tests), offering opportunity for cross-checking, and will hopefully average out interpretation bias amongst people with different focus and areas of expertise. This could be done via public online cloud storage e.g. Google Drive / Dropbox / OneDrive.