I haven’t tried to combine two LinkedIn company pages, but I have worked with clients when they have needed to combine two profile and found that writing to LinkedIn through the online Help Center (ask any question to get past the first screen and then click the Contact Us link). Explain to them specifically which company page you want to keep (with url) and which one you want to lose (with url) and ask if you can keep all of the followers (hopefully yes … my clients were able to keep all of their connections so it might be the same type of functionality). Usually they are pretty responsive and handle things accurately.
As far as when to make the switch, I would say the sooner the better so that the problem won’t compound with more and more followers that need to be converted. I’ve found with branding it’s better to go bold and consistent rather than maintain two brands so that the audience/customer base won’t be confused. The good news with LinkedIn Company Pages is that you can feature various products and services (with images) so you can promote the best products for each former brand to help alleviate confusion about where those products went. 

And finally, I would suggest sending a mass InMessage to all of the followers of both companies (along with potential clients/your other connections) announcing the merger. Include a link to the Company Page and ask them to check it out. If some of them need to re-follow the new company, explain how. You can send up to 50 InMessages at one time and you can send multiple InMessages and target who you want to send them to by location, industry, etc.

Kathy BernardGetajobtips.com