Yes, I can understand the frustration. Especially when you visited the campus, like it there, the city, the ambience and all that. But shutting down one door may open few others. Who knows, they may increase the intake numbers from the EAP route. By the way their Bio med eng major is one of the top notch programs in the country, in case if your daughter is interested in that line and wants to club it together with the EAP option.
But then one can never be sure of EAP route either as you have alluded. The slots are very few and the numbers of applicants with excellent gpa and ecs far too many. As a reference I am reminded of this poster here till last year. S/he was a very strong critic of BS/MD programs in general (probably may be because their child did not get in the first place?) and used to advocate that anyone worth their merit should only go traditional route. Apparently his/her child had a high 3.9x gpa till sophomore year undergrad (just short of 4.0 by a hair line) and was highly hopeful and confident of getting into their EAP program at that school. Turned out that s/he (the child) wasn’t even called in for an interview for the program (the parent was blaming on missed EC opportunities due to covid and what not, but shouldn’t it affect all others as well likewise?).
Anyway the point is better not count on getting in EAP route no matter how accomplished one may view of self. Consider all factors while selecting a school, with EAP being just one among them.