Larwood wasn't available to play againts anyone, so for subsequent tours he couldn't have been considered as part of a first choice attack.
Regarding Hammond and pace bowling, One England and to a lesser extent The W.I had viable pace attacks, and since Hammond couln't have faced his own, the only true test againts fast bowling was againts Constantine and Martindale and at the very least he was found wanting and was known to be quite uncomfortable againts them and wasn't fond of the short stuff.
One needs to be careful and examine the record of the players from an era, where they were only two strong teams and records were often inflated from feasting on the minnows. It was well known, even when Hutton was making his world record score that he referenced Bradman's record rather than his team mates because Hammond's wasn't seen as the true record because it was made vs New Zealand.
You clearly are not willing to concede that Headley didn't face England's first choice attacks. An attack doesn't consist of one or two bowlers, it means a whole attack.
The only time he faced a complete first choice attack was in the first test of the 1933 series against Macaulay, Allen, Verity and Robins. He scored 13 and 50. Second test in which Allen didn't play, 169 and 24. Third test in which Nicholas, Clark and Marriot were the bowlers, he scored 9 and 12.
In 1930, the attack was Voce, Haig, Stevens, Astill and 53-year old Rhodes. Against Australia that year, the attack had been a mix of Larwood, Tate, Tyldesley, Allen, Robins and Geary.
In 1934/35, the attack was a mix of Farnes, Smith, Hollies, Paine and Smith. Earlier that season, the attack against Australia had been a mix of Farnes, Bowes, Verity, Allen, Clark and Geary.
There is something here, unless I am mistaken.
Regarding Hammond, yes he did struggle against Constantine and Martindale. The Australian fast attack was quite woeful during this period, with only Tim Wall being the decent pacer.