Get the Kenmu Restoration to succeed, maybe by Go-Daigo enlisting the peasantry against the feudal lords who were his opposition. Unfortunately, Go-Daigo was a romantic who wanted to be in some eternal Heian era. A Kenmu Restoration that succeeded past its initial stages would probably spark quite a few wars as well. Speaking of which, avoiding the breakdown of the system of the Heian era and thus getting an eternal Heian era would be an idea as well. It's been a while since I looked it over, but the agricultural system during the Heian era was breaking down by the end of it.
Mongols are another solution. A Mongol invasion doesn't need to succeed, but it needs to succeed enough to break down the Kamakura Shogunate much earlier than in OTL. Preferably the Mongols will succeed and put their own guy in place as Shogun, maybe while the Emperor is forced to pay tribute to China (Yuan) as King of Japan (which OTL certain Ashikaga shoguns did). Obviously any Mongol rule of Japan will be only a thin veneer, with Japan as a vassal to the Yuan, perhaps like Korea. When the Yuan Dynasty collapses, obviously a new regime will rise in Japan, and hopefully it could be a strong enough regime led by a Go-Daigo type figure or otherwise a shogunate which actually does something good and doesn't just sit around like certain Ashikaga shoguns (Yoshimasa...)
Speaking of Yoshimasa, we obviously need to do something like the Higashiyama Culture which Ashikaga Yoshimasa helped create, but I think such a thing or a suitable equivalent would've come in phases if a stable Japan (i.e. the situation rebels sacking Kyoto while the Shogun just watches doesn't exist) existed in the same timeframe.
There was always the issue of successful nobles being rewarded land, and they didn't get any when they beat the Mongols OTL. As I've said before, the Shogun needs to retake his mantle as "barbarian subduing general" and subdue Hokkaido and Karafuto, which would give plenty of land.