Heather,
First off, I'm so glad that your daughter is doing well in Bigger Hearts! Getting her correctly placed is actually very important. So, you have a great start with her!

Next, if you're new to HOD it can take a bit of time to get a couple of programs going, so it's good to allow yourself some grace there. It does sound like from what you've shared that your 6 year old is not quite ready for all of the meat of LHFGH, so there's nothing wrong with just doing the phonics, math, handwriting, and Rod and Staff workbooks with him this year. Then, next year, he could head into all of LHFHG with the first grade options.
In all honesty, the Bigger Hearts year is an important teaching year that will really pay off big dividends in independence in later HOD years. So from my perspective, that's a good place to put your focus this year. Then, you'll also have your 6 year old's most important bases covered with the phonics, math, handwriting, and fine motor skills workbooks.
I'm wondering if you are using one of the phonics programs recommended in LHFHG or are using your own? While you can easily use your own phonics, many phonics programs add quite a bit of time to your day. If you're going too long with your 6 year old, you may wish to give The Reading Lesson a look. It is short and sweet and gets the job done, taking about 15 minutes a day. It is also open and go.

Just a thought.
I'm also wondering if you are using the Singapore math that goes with LHFHG? While you can again use your own math, it often adds time to your day. The Singapore math that goes with LHFHG takes 15 minutes a day. So, if you do go the HOD route in phonics, math, handwriting, and fine motor skills, you can expect all of those areas to add about 40 minutes total to your day for your 6 year old, which is very doable.
One last thing you could consider would be to do LHTH with both your younger child while having your 6 year old be the helper. LHTH takes 30 minutes a day and would give your 6 year old a healthy dose of the Scripture. So, by doing LHTH and the recommendations I listed above, your 6 year old's school day would last 70-75 min. total, and you'd also have your preschooler done during that time.
Just a thought! I wouldn't pull your 6 year old through LHFHG, as there is much to enjoy within it. Just let him grow up a bit, and I think you'll find a year of maturity does wonders!
Blessings,
Carrie