The people of the Hovenweep area were strongly influenced by the people of Mesa Verde. But they spoke a different language and seemingly didn't want to bear the yoke of that other control. Lumped in with Hovenweep I'm including the Canyons of Ancients area in southwestern colorado and the Dolores River Canyon area just to the east.
Like the Keres-speaking people of Mesa Verde, they abandoned the surrounding area about the same time. Some of them went east to the Rio Chama Valley, then south to the Pajarito Plateau. Others dropped south through the San Luis Valley while still others went further east and descended to the south along the eastern slopes of the Sangre de Cristo Mountains. A very few went southwest to the Hopi mesas.
These are the people I suspect may have become today's Tewa speakers, and I have alignment with that from a few sources.
Those who migrated south through the Ojo Caliente and Chama River valleys built Poshuouingeh, among other abandoned pueblos. Eventually, they moved up into the Jemez foothills and started pushing the Keresans who were newly there to move south. Eventually these Tewas occupied the areas where Puyé and Tsankawi pueblos were, before they moved down out of the hills and to the Rio Grande.
Others from the valleys to the west and north of Mesa Verde also migrated to the east, over the spine of the San Juan Mountains and down into San Luis Valley where they followed the Rio Grande south, eventually coming to the confluence with the Rio Chama and settling there.
Still others passed beyond the San Luis Valley and over the spine of the Sangre de Cristos before dropping down onto the western Plains where they mingled with some Plains tribes and learned how to hunt big game (deer, elk, bison, pronghorn antelope), preserve the meat, cure the hides and use the rest of the carcass. After a hundred years they drifted back west of the mountains and settled into the area around where the Nambé and Tesuque Rivers join with the Rio Grande, and divided into the pueblos on the east side of the river we now know as Pojoaque, Nambé and Tesuque.
For several decades in the early 1100s, there was a burst of construction in the Dolores River drainage. And just as quickly as that construction ramped up, it ramped down and the drainage was almost completely depopulated, never to be occupied by Puebloans again. When the BLM located their "Anasazi Heritage Center," the site turned out to be almost on top of several abandoned roomblocks and an old pueblo (Escalante Pueblo).