A 3.4 GPA is going to make you have to do very well on the MCAT and have a strong extracurricular resume to be a very competitive candidate. I think that the 3.4 at UVA would hurt less than the 3.4 at JMU however. Ultimately, though, if you do well at either institution it’ll be good for your application.
“However, I would truly like to attend UVA (but a more important priority would be a better resume for med school).”
UVA is a great school, but it won’t be so much harder than JMU that it should hurt your application. If you don’t have as much time for extracurriculars the solution is simple — pick one or two and become very involved in them and do something special with them rather than trying to do 50 different things at once. Use the summer and winter breaks to get research, volunteer, and clinical experiences. If you really want to go to UVA, don’t stay at JMU for another three years. You will do your best where you are happiest. That may sound trite, but it’s flat out true.
In terms of name, “UVA” will mediate lower grades better than “JMU” will, but not as tremendously as you might think. UVA does have a great med school though and coming from UVA undergrad might help your chances to get into their med school.