I am so glad that you are getting a chance to talk through options for your busy family! Some great suggestions are already being shared.
In looking at your line-up of kiddos, I had a few thoughts that may be worth pondering.
First of all, I am not sure how your oldest does with school but would there be any way for that child to do a 30 minute school time with your 6 year old each day? I know my older sister (who has 7 children) had her oldest daughter do this with LHTH with her little one. They had so much fun! It was a great change of pace for her oldest daughter in her day too. They just set the timer for 30 minutes and got as far as they could in 30 min. Then, the next day they picked back up where they left off. If this is a possibility, you could have your oldest do the left side of LHFHG during this 30 minute time with your 6 year old.
Then, maybe you could do phonics, math, and storytime with your 6 year old?
Perhaps you could have your RTR child do a 30 minute playtime with your 3 year old to gain you needed work time with your Bigger Hearts kiddos? I had my older boys do a 30 minute "playtime" with my littlest son when they were in high school. I still have my third and fourth kiddos do a 30 minute recess play break in the basement during school now (and they are a junior in high school and a 7th/8th grader). They both love it and look forward to it!
Another thought I had was that it may work to do a common math work time? We have done this before where the kiddos who need help with math do it in one room, and I moved around to be available to all during math time for any questions. It worked for a season at our house and may work with your Resurrection to Reformation, Bigger Hearts, and Little Hearts kiddos in one group. I put them spread out at varying tables and at our counter and spoke very quietly when helping them so as not to interrupt the others. Any formal teaching of math, I did further away first in a different room so as not to derail them all.
We have done this same strategy for grammar and composition in some seasons, teaching grammar first away in a different room and then joining in one group to work on writing and grammar assignments at once with me nearby to help as needed. You could try and see if either of these may work?
Another possibility would be to do just one read-aloud for your RTR and Bigger crew. You could omit the storytime from RTR and read-aloud the Bigger storytime books to all of them. Or, you could consider doing the RTR read-alouds with all instead.
Or, depending on your goals for your RTR child, you could consider going half-speed with her for a season as she eases into RTR. That would allow her to have a strong start to RTR, give you more time to work with your Bigger Hearts kiddos, and make sure your 6 year old gets underway in LHFHG.
Or maybe you could have a mother's helper come three times a week to do 30 minutes of school with your 6 year old and do 30 minutes of LHTH with your 3 year old? The mother's helper could do studied dictation with all too and maybe grammar too. Straight forward subjects work well for this. The mother's helper could be a new homeschool graduate looking for a few outside hours or an older grandma person. My sisters have each done this for a couple of years in their life during their busiest seasons. Maybe there is no one you know who could do this, or perhaps there is no funding for this, but it may be worth a thought for a season.
Or maybe your husband could do grammar with one set of kiddos at night? Or perhaps he could do one of the read-alouds before bed for Bigger or RTR? Or perhaps you could have your mother, or mother-in-law, or an aunt record the storytime books? I had my mother-in-law record herself reading aloud the storytime books in our early guides for multiple years. She volunteered to do it. I sent her the books and she recorded. My boys loved listening to Grandma Jackie read!
Plus, I could use the recordings again with my next kiddos coming up!
Anyway, just a few ideas that you could ponder to see if any might work.