An amendment:
Since I gave UVa credit for barely missing my criteria for being a Near-Ivy, I should give Bryn Mawr and CMU credit as well, since they also just barely miss.
Rice just barely misses my criteria for being an Ivy-equivalent.
So the revised list (with schools that barely miss in parentheses):
HYPSM:
HYPSM (Williams, Amherst, and Swarthmore). WAS LACs are the only schools close to HYPSM. 5 RUs and (maybe?) 3 LACs
(non-HYPSM) Ivy+Ivy-equivalent:
Other Ivies + Northwestern, Chicago, & CalTech, Duke, Cal, Pomona, Barnard, Wellesley, Haverford, Bowdoin, Wesleyan (and Rice). 11 RUs and 6 LACs
Near-Ivies:
JHU, Georgetown, Oberlin, Middlebury & UMich, Notre Dame, Tufts, Vassar and Reed (and UVa, CMU, and Bryn Mawr): 7 research universities and 5 LACs.