Though the comments regarding absolute phase/polarity inversion are not recent, I wanted to post a long term update on my experience with the option. I've used the Tortuga LDRxB with the phase inversion option now for a couple of years and have auditioned it in various systems.
The degree of difference between "normal" versus "inverted" is much influenced by the quality of the bass drivers in your speakers and the control provided by your amplification. With more rigid, fast, controlled drivers there is more difference between the normal/inverted setting than with drivers that exhibit a higher amount of flexing. Similarly, using an amplifier that does not adequately control the drivers, there is less difference. However, with well controlled, fast drivers with a higher Young's modulus (ratio of stiffness to weight), the correct setting is obvious. Regarding the terms "normal" and "inverted", these are relative to your system's configuration. Each gain stage inverts phase. Whether you attach the red speaker cable to one terminal or the other inverts phase, etc..
Once you've lived with the Tortuga LDRxB with the phase inversion option, you'll find that you can tell if a recording is correct or needs to be inverted relative to your system's acoustic polarity without even having to test the normal/inverted setting.
A key feature with the Tortuga is that you can switch between phase settings with the remote from your listening position. The other great feature is that you can at the same time select (also from the remote) between the various input impedance settings that best suit your system and the recording. In my system, just changing from one impedance setting to another only 3k higher or lower modifies the flavor of the sound and I frequently switch to the setting that gets the most balanced, natural sound from a recording whether it was recorded last year of half a century ago.
The Tortuga is an exceedingly transparent and revealing tool. Not having any gain stages, capacitors,switches, or potentiometers is something to hear. The features of absolute phase control and custom input impedance settings (all from the remote) are features I would now not be without. Add that it is a bargain compared to the sonic competition.