You should be able to continue Singapore and the other English curriculum you are using, as well as DITHOR at your child's pace.
Yes you will still do read-alouds for her as those are a key part and not the same as the Reading portion (DITHOR). You read aloud books that are higher reading level, and listening to books read aloud helps children understand tone and inflection and how to read smoothly, and helps cement things like grammar. Also you have the chance to immediately interact with the child and gauge their understanding of what was read. Listening to something, comprehending, and retaining it is a different skill than reading and retaining (one I am admittedly not very good at because I was a good reader and so my parents rarely read to me after I learned to read).
Storytime is when she will be learning story elements and analysis along with character traits that you will read a Bible passage and then look for whether your book's characters exhibit these qualities or not. There is some similarity with DITHOR but this is meant to be done all orally with the child.
Extensions are books the child can read themselves and provide deeper learning on the history topics. Inventors are covered and some history that goes into the 1900s but WWI/WWII are not covered.
If Bigger Hearts is where she places and she is the only one you are trying to place (not combining with another child and that's why you are putting her in a "lower" level) then that's where she should be. Have you looked over the placement chart?
http://www.heartofdakota.com/placing-your-child.php
I would like to beef it up for her and want to get some thoughts.