For your own sanity's sake, I would personally recommend against deactivating and reactivating your computers in order to use three devices.
You are correct in that you'll have to purchase an additional subscription if you wish to use a third device. Currently however, all Creative Cloud subscriptions require a separate Adobe ID, so you will have to manage two accounts if you decide to purhcase two memberhsips.
From this Adobe ID FAQ page, I did find a section stating that you can contact customer support to consolidate mulitple Adobe ID's. However, I am not sure if you can do this and still preserve your two CC subscriptions. You may want to give customer support a ring to find out if this is possible.
To contact customer service, go here: http://helpx.adobe.com/contact/
- Select Creative Cloud as your product
- Select "Managing my membership..." from the next dropdown menu
- Click "I still need help"