Florence,
This is a tough one. If your other kiddos were doing Bigger Hearts, I'd be quicker to suggest just allowing your 11 year old to join in for the left side of that guide, in place of Preparing Hearts. However, with your oldest being 11, and the target range for Beyond being ages 6-8, it is just too far of a jump back to really cover the skills needed by your almost 12 year old.
I agree that the Learning Through History side of Beyond can stretch for older ages and that the material is interesting (even to me as an adult), however the corresponding activities are not going to be what an 11 year old needs. Perhaps, you could schedule your older one's history project to be done at the same time your other kiddos are doing their hands-on activity in Beyond? Then, they could all work around the table on their hands-on thing at once. Or, you could have your younger ones join in on your older one's projects from Preparing? (Only if it's alright with you that they'll do the projects again in a few years.

) Maybe it's just the social sharing with his siblings that your older one is missing.
My 9 year old loves narrating his science to his 6 year old brother. The 6 year old has even made a constellations book too, along with my 9 year old. My 9 year old shows the 6 year old all his experiements for science too. He loves having an audience (and the 6 year old is enthralled). Just some food for thought!
Blessings,
Carrie