The state of art for sunflower system
the Erdos sunflower conjecture seems to be very difficult after now over a half century(!) of being open. youve already listed some of the very best and most recent refs on the subj that would be very hard to beat (Alons recent paper, Juknas book on combinatorics). the Alon paper is highly notable for newly linking the conjecture to lower bounds on matrix multiplication, an area that has seen recent groundbreaking advance in the Williams results.[4]

you can find some further treatment, mainly applications to extremal circuit theory (circuit lower bounds 1st discovered by Razborov &amp; extended by others), in Jukna's outstanding book [1]. 

one notable/related recent ref along these lines apparently not-so-widely-known-or-cited-so-far is [2] by Rossman with a new direction of application (Erdos-Renyi random graphs over monotone circuits) and who proves extended and/or stronger results on "quasi-" sunflowers. the paper is a result from his Phd thesis [3]. from the paper abstract


  We introduce a new variant of sunflowers and prove an analogue of the sunflower lemma that may be of independent interest.


[1] Boolean function complexity, advances and frontiers

[2] The Monotone Complexity of k-Clique on Random Graphs (2009) Rossman

[3] Average-case complexity of detecting cliques by Rossman

[4] Commentary on Williams breakthrough on matrix product lower bound RJ Liptons Godels Lost Letter blog

[5] Detailed Materials on Sunflowers