I'm glad she has loved the Thorton Burgess books - they are so good, aren't they?!? Of course, there are many more titles of these available. The only thing is, it is really important to have dd develop the skills that are taught through the daily plans of LHFHG's Storytime. They are the following...
*Day 1: basic comprehension discussion questions
*Day 2: retelling the story in a variety of ways
*Day 3: critical thinking questions including some vocabulary discussion
*Day 4: early writing practice emphasizing names and simple words
*Day 5: moral connection questions with personal application
These are tough to replace or to tweak to duplicate. They provide reading instruction that goes so much deeper than just listening to a read-aloud. I've really been thinking about your question here... and personally, my dc have heard/read the Burgess books many times over, and loved them each and every time.

If it were me, I'd probably reread the Burgess titles and do the plans with my child even if she'd heard them once before.

Listening for enjoyment (as dd did this year), and having to be personally responsible for skill-based learning along with the listening (as dd now would do when LHFHG is providing her learning) are 2 different things, and the latter will prepare her better for what is to come in Beyond. She could still listen in on the Beyond Storytime with big brother for "new" listening material, while still hearing her Burgess books for "learning" material. Then when she does Beyond, you can just use one of the other 2 sets with her. However, you will know best here! I just know I appreciated the learning that took place "skillwise" along with the Burgess books that year, as well as the fun reading the wonderful Burgess books provided! I hope something here helps!
In Christ,
Julie