I'm pretty sure that this PR added the ability to set the units for the tabular reports separately from the SQL output file. In v9.5.0 or later, you can set the 'Unit Conversion' input in the OutputControl:Table:Style object to 'InchPound', which will result in a tabular report in IP units, but the SQL will remain in SI, allowing the openstudio results measure to do its thing.
You should be able to set that input with a simple EnergyPlus measure.
Edit: you also have to set 'Unit Conversion for Tabular Data' in Output:SQLite to 'None'. I've verified that an EnergyPlus measure with:
oc = workspace.getObjectsByType('OutputControl:Table:Style'.to_IddObjectType)
oc.each{|o| o.setString(1,"InchPound")}
os = workspace.getObjectsByType('Output:SQLite'.to_IddObjectType)
os.each{|o| o.setString(1,"None")}
will produce a tabular HTML report in IP units _and_ an openstudio_results report in just one simulation.