Well, I have been playing 1.c4 for as long as I can remember and here's my two cents:
1- First off, forget about the Jaenisch Gambit. I don't see how Black may EVER get to play for a win after 2.cxb5 a6 3.bxa6 Bxa6 4.Nf3 Nf6 5.g3 e5 6.Bg2 d5 7.O-O c5 (fun fact: your win rate in this position is 0/3) 8.d4.
2- Kramnik-Shirov Counterattack is okay by itself but 2.g3 is a very pleasant way to avoid it which I play exclusively for this very reason.
3A- In my opinion, the most challenging lines are the ones starting with 1...e5 2...Nc6 3...f5. The good thing about most English lines is that White does not really have much but Black has problems - here, though, White has problems too and it's game on.
3B- 1...e5 2...f5 is also playable with the idea of meeting d2-d4 with ...e5-e4?! which is not possible in the lines starting with ...Nc6. Although I would rather not allow d2-d4, I would not necessarily worry about the fact that the engine does not particularly like the resulting position after d2-d4 ...e5-e4 either. The resulting structure is far from easy for White to play. Take the following position as an example:
White is an exchange up but Black has the semi-open f-file to work with in addition to the French Structure with the colors reversed. I tried to beat some strong bots (2200-2400 rated) from this position onwards and let me tell you, it's mind-blowing how fast the initial evaluation of +1.4 goes down.
Hope this helps.
I was wondering if anyone had any statistics on the highest win rate % opening against the English (1. c4) I've always somewhat struggled against it, ive tried multiple different openings such as the Kramnik-Shirov Counterattack, and the Jaenisch Gambit (as i play the Benko Gambit). But it just feels like no matter what i do, im left not really understanding the English and always at a disadvantage. Granted i did check then, and i am 46% to 46% win rate with the Jaenisch Gambit, but i still feel im always at a disadvantage using that opening, compared to the Benko where I have serious compensation.
Any help would be much appreciated, im OFTEN a more tactical/aggressive player, but I am not opposed to more positional openings.