I could not get both the Stowaway keyboard and mouse to work simultaneously. Maybe you'll have better luck.
Just for grins you might try the drivers for the Freedom Pro keyboard with your Stowaway keyboard. I put my Freedom Pro in SPP mode but bluetooth settings shows that it pairs (but does not connect) as an HID device, not an SPP one. Once it paired you get it to connect under the keyboard settings - input method, not in bluetooth settings. It never shows as connected under bluetooth even though it is. I speculate this is way I am then able to quickly and reliably also connect mouse under bluetooth settings as they don't interfere with each other.
You can get the Freedom Pro drivers at
Again I have not tried this as I do not want to risk losing what I've got and did not remember about the Freedom Pro drivers until I recently also got a Freedom Pro keyboard.