Taking into account I know nothing about your children apart from what I just read in your post take everything I say with the proverbial grain of salt!
I would totally agree though that getting as firm a handle as possible on your children's underlying challenges will hopefully assist any transition between schooling types. I like having lots of information.
We don't have these challenges, we have others but not these specific ones. I do have friends who have a son and daughter who are PG, have been homeschooled since sixth grade and are now transitioning back to year 10. Part of the reason is driven by the son desiring a wider group of friends. They have moved to a bigger city so their options for schooling have also improved.
The benefits they have discovered of returning to school are that the children are of an age where they can now access lab based science classes at a more interesting level, there is a greater range and choice of subjects so they can appeal to the kids interests more, the other students are older and there is a greater tolerance among some for the quirks of my friends kids. This may be a function of the school chosen because not all teens are tolerant. So it can be done.
I don't know if it will be true of your son but our daughter drastically improved her organisational skills once she hit high school as she had to but she was also able to model what the other kids were doing. sometimes increasing demand and expectation can result in growth. I don't know how your son would respond but maybe he hasn't improved in some areas because the pressure to do so isn't there while he is homeschooled.
I can imagine the thought of the transition is very stressful for everyone. I think your plan to have your children assessed is wise. Information is useful. Looking at different schools and visiting them to get a feel with you children is also important. I hope you have a few options.
I posted a resource about slow processing on another thread. It is often associated with ADD and similar problems so may help.
http://www.mghclaycenter.org/parent...oping-slow-processing-speed-home-school/This blog is from an educational psychologist and might be interesting. I found the comments from other readers had a number of people with teens they were worried about. Apologies if the references aren't relevant.
http://bitsofwisdomforall.com/2011/10/29/finding-the-right-help-to-build-processing-speed/