Is there any reliable, timeless(I assume that this phrase is an
example of “dead constitution”) interpretation?
The Black's Law Dictionary (4th ed.) defines High crimes and misdemeanors (in its entry for Crimes) as
immoral and unlawful acts as are nearly allied and equal in guilt to
felony, yet, owing to some technical circumstance, do not fall within
the definition of "felony"
(citing U.S. cases).
Also, searching for "High crimes and misdemeanors" at leagle.com displays decisions involving that term. Although I am unsure whether any of the search results elaborates on the definition, one can certainly identify how the term relates to other concepts.
For instance, District of Columbia v. Trump, (Civil No. PJM 17-1596; Jul. 25, 2018) in its footnotes 23 and 31 reproduces a Constitutional provision which mentions the term. Locating where footnote 23 is referenced in the court decision, it reads that that article of the Constitution "already addresses the crime of bribery, making it an impeachable offense". Thus, one can infer that bribery is one example of high crimes and misdemeanors.
Some say that impeachment is “what congress wants it to be” but I am
inclined not to accept this
That notion does not seem far-fetched. See Nixon v. U.S., 506 U.S. 224-227 (1993), stating that "On May 10, 1989, the House of Representatives adopted three articles of impeachment for high crimes and misdemeanors.". And, going back to District of Columbia v. Trump ruling, the same paragraph referring to footnote 23 depicts as
"highly unlikely that the Framers would have intended bribery to be
both an impeachable offense and, at the same time, an activity
Congress could consent to when a foreign government donor is involved"
which reinforces the notion that the Congress can determine --by consenting-- that certain act is not an impeachable offense, and hence not a high crime/misdemeanor either.
One of the main points I intend to make here and in other answers is that legal dictionaries like the Black's Law Dictionary and other free, online resources such as leagle.com can take you far when you need to conduct legal research.
Edited to add reference (per OP's comment 8/10/2018)
Two days after answering this question, libertylawsite.org released an article that provides historical context as well as references on this topic.