I would assume the code base and various tools and technologies will remain the same, thus an extremely thorough functionality test might not be required. Also my assumption is that you have separate infra for each company, for all apps, in place.
1. Data split is of prime importance in your case.
a) For each of the eight apps, categorize the nature of data based on the rationale of the company split (product lines, services, internal departments) and the user base. It is easier said than done but this will be a major effort area for you and your team.
b) Plan the split on production servers for both the companies meticulously keeping in mind the sensitivity of the data and the time bounded activities that need to be undertaken by the user base (BAU app processes) in both companies on their respective data sets.
2. Test and then test some more...
a) Copy over current production data to your test servers after your data analysis is done and split the data based on the scheme/algorithm/script that you come up with.
b) Validate presence, absence, inadvertent presence of data. Have respective application user community play around with this along with your system testers.
c) Validate major processes that use these two data sets.
3. Team org.
Suggest your project manager to divide up your existing teams working on this effort as if they are working for the split companies. This will channelize their effort towards the end goal.
4. TIme
If you have started out just now, then time is probably not on your side and I hope that applications are not too complex. As a BA/Lead you can always ask for better and practical timelines to your management. You just have to make your case valid with effort/estimate numbers.
Let us know how it goes. Best of luck!