Sorry Pierre, but I do not really understand what AMR actually does.
Other information I saw on their homepage were not reassuring either. Tech specs were far from being brilliant.
I’d recommend to carefully read the series of posts from dCS’s James Cook about DAC and clocking in this thread:
(dCS Ring DAC - A Technical Explanation)
The bottom line: My recommendation for your upgrade project would be to look for a (second hand) dCS DAC.