Data for the 2SK97 so far is that provided by
this thread. Also, in
this site you may find a compilation of data for lots of transistors, including the old jfets. The 2SK185 is very likely two 2SK43 in a metal can (but not the 2sk43S) . Note the similarity in their parameters and dimensions. Also, note that both are made by Sony. (the 2sk121 is similar single jfet, but unobtanium) You may find 2sk185 rank 2 in Japan still today and i believe they are an excellent option if you can get them. This is a matched pair which is better than trying to match by hand (need to buy about 10-20 single J113 to build two matched pairs for left and right channel, and this will end up costing you the same as one pair LSK389).
If you look at the 2SK97 parts that people show in the pictures in this forum, most of them are rank 2 and fewer are rank 3. This rank obtained by the Idss parameter. However, the gain of the jfet is determined by the value of gm which in turn correlates with Idss. There is thread in this forum where
Echowars "profusely stated" that gm is very important to prevent saturation of the response of the input differential pair.
Finally, what I learned about jfets in the book by Horowitz and Hill is that some switching devices did have accidental low noise performance, I recall the J107 being one example mentioned in that book, but
also here. Some RF jfets like the BF862 (discontinued) and may be the CPH3910 (you may want to read articles and the book by Phil Hobbs) turned out to be surprisingly good too But for that matter the 2sk209 may be a better option. In some instances the sources of the two jfets are conected together, and in this case you may resort to the Toshiba dual 2sk2145 or the ON parts mentioned above. If you look at the datasheet, the option of a pair of 2sk209 is ok from the point of view of their paramenters and noise characteristics, but thermal tracking is hard as it is difficult to glue togehter a pair of 2sk209.