I've been reading Pat Pranke's 2004 dissertation at the University of Michigan, an annotated translation of the Vamsa Dipani, a history of Buddhism in Burma, or more correctly I guess, western mainland Southeast Asia, since a lot of the history took place when Lower Burma was under the control of Mon elite, both religious and political, and under one king Dhammazedi, both religious and political.
From 1331 to 1475 several missions of monks were sent from mainland Southeast Asia to Sri Lanka. These missions sought reordination in Sri Lanka so they could start new reformed monastic lineages that could be traced back to the time of the Buddha. In 1475 the last and most famous of these missions was sent by the Mon king Dhammazedi (r. 1458? -1492). According to the scholar of Buddhist history Patrick Pranke:
"King Dhammazedi appears to have been especially influenced by the religious policies of the Lanna Thai king, Tilokaraja, who was his senior contemporary. In addition to promoting the reordination of monks according to the same Kalyani method, both kings in emulation of Asoka, sponsored the planting of Bodhi tree saplings throughout their realms, and both built as monuments at their capital replicas of the Mahabodhi temple replete with even stations (marking the seven weeks the Buddha sojourned at the Bodhi tree)" (Pranke, 2004, 214).
Pranke's translation also covers the religious reformation that accompanied the reordinations, eliminating secular practices among monks. Perhaps there was some breaking up of what amounted to monastic estates. Pranke mentions the breaking up of Sri Lankan monastic estates during the 12-13th centuries (Panke, 216). Sort of like King Henry VIII, the ex-monk arrogates the wealth and estates of his former colleagues. Actually, Harvey mentions that his female predecessor had put too much lands in the hands of monastic institutions. He took it away, but tried to make amends for his actions through religious donations. Will have to check what Harvey's ultimate source is. Anyway, there seems to be a high concentration of royal power from Shin Saw Bu through Dhammazedi. Enough surplus and religious wealth accumulated at the center, at least, to create the biggest copper bell in history. Was Razadarit the initial impetus for this concentration of power in Lower Burma? Maybe the Mon region consisted of low population, culturally rich, but militarily weak localities before Razadarit. Sure would like to see archaeological work done in this region. Hasn't anyone done preliminary surveys? What about aerial surveys?
In addition to paying attention to the economic dimension of monks' lifes in his reforms, the Nidana Ramadhipati Katha has Dhammazedi debating how not to violate the monastic code of conduct [Vinaya] in his own military conduct when rescueing the Mon queen Shin Saw Bu from Ava after she was taken captive by Ava troops. OK, the narrative here seems rather fictional, but Dhammazedi is once again portrayed as a king who pays meticulous attention to the details of religious practice, apparently like the Lanna king Tilokaraja.
Mon historical works certainly have frequent references to the Tai polities of Ayutthaya and Chiang Mai. With Dhammazedi ruling to 1492, that's quite late. Only 50 years before the radical transformations/consolidations of Bayinnaung. More Mon references to Chiang Mai and Ayutthaya than in Ava's Upper Burma history.
The route that Chiang Mai and Ayutthaya used for missions to Sri Lanka must have passed through Tennaserim very close to the Mon region. This is probably why there was more contact. Was Tennaserim more important for religious contact with Sri Lanka before it attained importance for trade? Did religious contact open the way for trade and eventually the military expeditions of Tabinshweihti and Bayinnaung? Will have to look at the writings of Thai scholars, especially professor Sunait Chutintaranond of Chulalongkorn University who writes on this subject, I believe.
Although Mingyinyo (r. 1486-1531) and Tabinshweihti (r. 1531-1550) had contact with Sri Lankan religious traditions (See here), they don't seem to have had contact with Chiangmai religious traditions as Dhammazedi (r. 1458-1492) did shortly before. Perhaps there's a a little bit of geographical determinism here. The isolation of Toungoo protecting them from Shan/Tai invasions and raiding from the north, but also lessening contact with Tai polities from due east due to the mountain barrier and the abscence of any religious motivation to cross the mountains.