Congratulations! Getting into top UC engineering programs through the CCC route is a big accomplishment!
It really sounds like your best path is to take the Regents offer at UCI, which will save you significant money and give you a great education, and aim for grad school at Berkeley. As @ucbalumnus points out, ChemE at UCB outright says that they won’t accept their own undergrads to their grad programs. If I were you, I would save Berkeley for grad school, which is its greatest strength.
The Regents scholarship is not just about the $2500/year. You get priority enrollment, which is a huge, HUGE advantage at a UC. (Because getting the education you’ve dreamed of is all about getting into the actual classes you want, and that is NOT always easy as a UC undergrad!) Being a Regents Scholar will appear on your transcript and will add gravitas to your resume. There are other perks as well. http://www.ofas.uci.edu/content/regentinfo.aspx?year=2017&sp=1
(Also, since you’re interested in biological applications, it’s worth noting that UCI has one of the top Bioinformatics programs; if you have any background or interest in programming, adding some coursework in this field could really enhance your opportunities.)
You should not feel that getting your bachelor’s at Irvine is in any way a compromise. It is an excellent undergrad education in every way, and your clear path to a Berkeley PhD if that is your goal.