Funny....you state that his "best symphonies" are the first two, yet I know of no conductor or musicologist who feels the "Spring" Symphony is "better" than any one of the other three. The C Major and E-Flat symphonies are certainly his most mature and expressive.
I should have mentioned all the four. In fact I prefer and by far the first two, in special the second, but many people have other opinions, preferring the 3rd. The 4th has beautiful ideas but it's structure is poor, based in the thematic repetition, not in development (and the cyclic idea doesn't convince me either).
Regarding the opinion of conductors, remember Furtwängler, when he was recording the 4th.
Val, "hearing" actual influences from composer to composer is not that easy---can you hear Schumann's influence in Dvorâk or Elgar? That might be the test! As to Brahms' chamber music, I'm surprised you don't hear the "deep" similiarities with Schumann (with the exception that the latter is generally more inspired).
I was more concerned on the supposed influences regarding the composers associated with the idea of "musique de l'avenir", such as Liszt, Berlioz, Wagner.
I accept that we can see some influences in Tchaikovsky, Elgar, Grieg, but those influences appear, in general, in conservative composers: you can't find those influences in Mussorgsky, Debussy, Janacek, just to name some composers of the last decades of the XIX century and first decades of the XX.
About Brahms: there is an influence of Schumann, the same way there is an influence of Beethoven, Mendelssohn, Schubert. But Brahms, in special in his chamber music is so genial, so personal, that it seems absurd to try to dig here and there a little similitude with his predecessors.
You didn't mention other acclaimed great masterpieces of the Third Period: the 'Cello Concerto, op. 129; "Die Braut von Messina", op. 100; the first Violin Sonata, op. 105 (considered by many "the most important violin sonata since Beethoven"); also the "Maria Stuart" songs; the wonderfully poetic (and almost Brahmsian) "Märchenerzählungen" for piano, clarinet and viola, op. 134 (1854!), very nearly Schumann's last work. And Gidon Kramer seems to think the Violin Concerto is a masterpiece, but I wouldn't put it in the category of the Beethoven, Mendelssohn, Brahms or Tschaikowsky.
The first violin Sonata is beautiful. But, the best since Beethoven? And Brahms 3 Sonatas? And Franck, Debussy, Bartok, Enescu?
Agree with you in one point: I should have mentioned the Maria Stuart Lieder. They are great works.
P.S.: I have an idea, Val---go back to your recordings of these works (and anything else you have from the 3rd period) and listen to them again, this time pretending they're by Brahms. Who knows? Maybe something interesting will happen.....
I have the complete piano works. By coincidence I am listening them again, for the third time, but, since I have several versions it will take sometime to finish it.
Right now I am with the opus 13.
And regarding those masterpieces (Papillons, Davidsbuntlertänze, Carnaval, First Sonata, Fabntasiestücke opus 12. Etudes Symphoniques, Kreisleriana, Fantasia, Humoresque) I have no doubt: with Debussy this is the greatest piano music ever composed since Beethoven (and I am not forgetting Schubert, Chopin, Brahms, Liszt or Bartok).