>And the highs did sound veiled - quite noticeably so. Such a stark contrast with the HE400i's somewhat sparkly and forward treble.

The HD 6xx have a warm neutral sound, the treble is supposed to be recessed. HE400i is neutral but it does lean towards the treble. People could argue that it is a bright neutral sound so they would be polar opposites. You can easily compare them with this graph:

https://crinacle.com/graphs/headphones/graphtool/?share=IEF_Neutral_Target,HE400i_(2020),HD650_S2_(2020)_(fresh_pads)