See the post dated 7-30-2018 at the end of this thread
, by member "600ohms," who is Keith Herron himself. As you’ll see, bass rolloff would not be an issue with a 16K load, although a **slight** compromise in dynamics is possible. But my belief is that Keith is extremely conservative in making such statements, and consequently when he says that "lowest distortion and best performance occurs with output loading at or above 20k Ohms" it is likely that any such compromise with 16K would be imperceptible in most applications.
As I recall Keith revised his website page on the VTPH-2a to reflect the statements he provided in that post at around the same time the post was made. Although the manual still suggests 50K or more as being optimal, that statement apparently having been carried over from manuals for earlier iterations of the phono stage, possibly going back to the VTPH-1.
Also, in a post dated 7-17-2018 in this thread
Keith is quoted as stating as follows in an email to a member:
The output capacitors of the VTPH-2 and VTPH-2A are approximately 7 uF (polypropylene) and the low frequency response is RIAA flat down to 10 Hz (within 0.1dB) into a 10k Ohm output load.
7 uF (microFarads) is more capacitance than is provided by the output coupling capacitors of many other tube designs, and at 20 Hz and with a 16K load is a large enough value to be consistent with the 10x rule of thumb minimum guideline for line-level impedance matching, in combination with the 400 and 500 ohm nominal output impedances of the two versions of the phono stage that are presumably specified based on a mid-range frequency.
So I think you would be fine pairing the VTPH-2a with your integrated amp.
(VTPH-2 owner, used in conjunction with an Audio Technica AT-ART9 cartridge and a 50K output load).