We just finished CTC with our almost 11 yo, Beyond with your 7 yo, and half of LHTH with our toddler. Because my dc are far apart in age and ability, I actually found it less confusing to teach separately. There is such a gap between them that if I chose history/science even on the easier side for my oldest, it would still be confusing and over the head of my 7 yo. He would be asked on a daily basis to do things that are too difficult for him, which would in turn make the day drag on for my oldest. If I was going to combine the 7 and 11 yo, it would be better to do so in a younger program and up it with extensions, but even then - my oldest is well beyond the extensions of Bigger Hearts, which is definitely the highest guide my 7 yo could do. Same deal with my little guy. My 3 1/2 yo is a smart little cookie, but my 7 yo is leaps and bounds ahead of him. For these reasons, we've found it a huge relief to teach separate programs. The dc are together for portions of DITHOR, which works well for them, but separate for the rest of their schooling. We've occasionally done Storytime together, or a poetry sharing together of the different poetry their studying, but mostly they are separately working on things that fit their learning well. I am thankful they are learning the skills they need to for each of their different ages.
HOD is so strong on incrementally teaching academic skills, and that's what ultimately leads my dc to being able to independently do things for school well too. So, for example, Beyond did a good job of teaching my middle ds to orally narrate well. It modeled it, held his hand through that whole skill, and helped him learn how to properly orally narrate. Had he done Bigger Hearts when he was too young, he would have missed that needed instruction for doing that skill well because Bigger Hearts assumes dc are somewhat familiar/beginning level proficient with this skill already. Same thing with written narrations, summary narrations, detailed narrations, creative writing lessons, etc. Because all of these skills are incrementally taught, I can just say at certain guides "Do an oral narration" or "Do a written narration" or "Write a summary narration", and that's enough instruction because they've been taught well step-by-step to be able to do this. HOD always does a refresher of what's expected for each of these things, but it's assuming that a child is able to do the things noted in the placement chart well when entering a guide.
Many other curriculums that are for very wide age ranges just say "write a written narration" or "write a poem", etc. and never truly teach how to do it, I'm sure the idea being that everyone will just do it on their own level. But where's the instruction on HOW to write a good narration or a good poem? If there is not any instruction on this, how will dc progress? Many times the skills are just left out or are made to be so very general that anything will do for a product. I think HOD's method of making sure skills are taught when they should be taught, of keeping age ranges to about 4-5 years for guides, and of beefing up by adding extensions is a great way to combine across they ages. Of course there are exceptions to the "4-5 Year" range. There are times that an older child is struggling more while the youngest is flourishing, which narrows that gap and makes combining an excellent placement for all involved. Or, there are times when a very busy life, health concerns, many dc to consider, budget needs, etc. make doing 1 program for all the best choice because it is the one that will get done on a daily basis - much better than a bunch of programs not getting done day after day.
Your dc are quite close in ages to fitting that range, so only you can know if that's going to be your best fit. But I just wanted to share the thought that goes into the plans for HOD, and that the way the guides are written makes it easy to teach several programs at once. As the child matures, their level of independent work goes up, which it can because the skills have been taught and the things a child should be doing independently are assigned to be done independently. Meanwhile, the younger guides keep school time shorter, and focus on building a strong 3R's foundation. So, for CTC, my teaching time was around an hour or an hour and a half. For Beyond, my teaching time was around 2 hours or less, and for LHTH, 20-30 minutes. This made our school year very balanced, and our dc loved their year. Whatever you decide, I think you will find HOD to be a joy to teach and a blessing to your family. There is not one right decision here, but rather one right decision for your family, and only you can know what that may be. Thanks for your questions here, as they are so important and help others ponder their choices as well!
In Christ,
Julie
I started out the year doing Beyond, LHFHG, and LHTH and it still wasn't disjointed.... in fact it was easier in some ways, just not on my mind thinking I'd be doing back to back books forever. 
) But they all love the fun time they have in school every day! And they each do school for a very appropriate amount of time given their ages. My 9 yo last year needed to spend 4-4 1/2 hrs on school, while my 5 yo needed only the 1-1 1/2 she got. Garret who was only 3, joined us for about 30 min. The younger 2 had the time they needed to enjoy playing together inside and out. (And they still all 3 had all afternoon and evening to enjoy the company of each other!