Advice on transferring schools, chances for breaking into consulting

I completed my second year at Columbia and I'm strongly considering transferring. My grades are alright and I have extensive prestigious internship and extracurricular/leadership experience. Overall, I was on track to be in a good position to apply to tier 1 and tier 2 consulting firms out of undergrad.

However, I was assaulted at school and developed PTSD that severely limited my abilty to function on campus and negatively impacted my health. My grades took a hit during this time (GPA dropped 3.8-9 to 3.4-5 in one semester) and I ended up taking medical leave during what would have been my third year to get my health in order. At this point, I think it would be best to transfer to a school that would offer a healthier environment and a better academic fit. I'm planning on sending transfer applications to Brown and Reed College, which both seem like they'd be good matches for me. However, I'm concerned that such a transition would negatively affect my chances for MBB or even tier 2 consulting firms. Brown seems to be less of a target, and while Reed is academically recognized and great for getting into grad school, it's a small college and not a target school at all. Transferring is the healthy decision in many respects, but I know I want to do management consulting and I'm worried transferring would severely hinder me come recruitment time. Would transferring to Brown or Reed completely cut off my opportunity? Any advice would be greatly appreciated.

For context: I plan to seek an MBA/Masters in Public Policy degree later on, and I'm also looking to transfer to a school that offers a public policy concentration (Columbia does not offer this to undergrads).