The Japanese did make preparations for the second invasion, but these were more aimed at making sure that a stronger force would be ready, rather than any real tactical changes. Preparations included:

1. More fortifications, including at Hakata Bay where the key fighting took place in the first invasion, and also at other likely landing places.

2. Better organisation of local forces, so that they could respond more quickly to an invasion.

Neither of these was tactically novel, and both had been used before to prepare for earlier invasions scares (e.g., when Japan feared an invasion by Silla and/or Tang China after the unification of Korea, in which they had supported Baekje, one of the losers).

There might have been a third important component of the preparation: making sure that there were ships/boats ready so that the Mongol fleet could be counter-attacked. This could be viewed as simply part of 2 above, but it did offer the chance to counter-attack, so could be viewed as a tactical adaptation. However, boats and ships were used in Japanese warfare, sometimes on a large scale (e.g., the Battle of Baekgang AKA Battle of Hakusukinoe (663), supporting Baekje against Silla and Tang China), so it wasn't a radical innovation.

Essentially, Japanese tactics had stopped the first invasion, and sensible preparations were made to use mostly the same tactics - with the addition of naval attacks - against a stronger second invasion. Since the second invasion was stopped successfully, there would have been little perceived need for any changes. After each invasion, Japan planned a naval counter-attack against Korea, but both times the plans were abandoned.

Therefore, your difficulty in finding anything about tactical changes might be in large part due to no significant tactical changes having been made. Worse, most of the primary sources say little about tactics, and some of what secondary and tertiary sources say isn't correct. For example, u/ParallelPain discusses the fairly common myth that Japanese soldiers had difficulty due to a tradition of formalised one-on-one combat in battle in

• https://www.reddit.com/r/AskHistorians/comments/gtnsi0/is_it_true_that_samurai_found_difficulty_fighting/

Another myth is that the Mongol invasions drove changes in Japanese weaponry, but the changes only appear well after the invasions, which I discussed in:

• https://www.reddit.com/r/SWORDS/comments/fg06wp/did_the_mongol_invasion_of_japan_lead_to_the/

You might also be interested in u/ParallelPain's discussion of the numbers in the invasions, complete with links to Chinese and Korean sources (unfortunately, in Classical Chinese).

You might be out of luck when it comes to this period, unless you know Japanese.

Surprisingly, western research on the period is rather scant.

Apart from Conlan's book, there is also an old phd out there (I think accessible via proQuest):

Kyotsu Hori. The Mongol Invasions and the Kamakura Bakufu. 1967, doctoral thesis, Columbia University.

Suffice it to say, the chapters on the whole political situation are bound to be rather unreflective of the current state of research.

Otherwise, you would have to see if you can get something out of Conlan's Weapons and Fighting Techniques of the Samurai Warrior 1200-1877. I don't have it, so I can't check what's in there. Also Karl F. Friday, Samurai, warfare and the state in early medieval Japan. Maybe Farris' Heavenly Warriors: Evolution of Japan's Military 500-1300 has a tiny bit on it too.

For pop-history, Turnbull would also have you covered, but I wouldn't cite him in a paper :)

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Oh, also, if you found some papers, I'd be interested in knowing which ones!