Sam, your experience is consistent with mine during 50 years with myriad amps and signal chains. More power, especially current, works better. One insight is that current lag induces phase lag. In most speakers phase lag is not audible, since phase is already compromised and the ear-brain is reconstructing - inferring the wave-form. But minimum phase transducers eliminate that fore brain engagement (because the wave-form is not phase compromised), and therefore any phase anomalies are much more apparent. Similarly holco's GD upgrade is more evident on Thiel (or other such as V'steen) minimum phase speakers.
I'm speaking from hard experience. Upstream transparency was the single most critical aspect of success or failure of Thiel auditions. The speaker always gets blamed for any musical failing. But if you think about it, the speaker is critically translating its input signal including phase response, which is why it can sound so good when the signal is right.