No it is not possible to circumvent it. Steam is proprietary software(which is why you have to press a "Buy" button even thought it is free)
You can make it easier buy clicking Reinstall Previous Purchases in the File menu. It should then show you Steam but you will still have to sign in to install it. In fact you should have to sign in to find your previous purchases. This method is easier because it will show you all your previous purchases(if you have any).
B.T.W. the reason APT and hence Synaptic cannot find it is that you don't have the software source enabled.
The Software Center can see the "For Purchase" software, even if you don't have the source available. The process in pressing the Buy button is:
Go to the Payment page(you must sign in to get to this page), the payment is skipped if it is free but proprietary software.
Add the software source to your existing sources
Do a source update(same as
sudo apt-get update command in terminal)
Install your software from the now available software source
When installing previous purchases it just skips step on and does steps 2-4. I didn't include it as a step but just like installing any software you will have to enter your admin. password to start the process. (You have experience in installing software so it was not needed, I only mention it here in case a newbie has the same question; I would not want them to be confused if I left to vague.)
Reinstall may not show Steam if you downloaded the Beta directly from Steam and installed it locally, in which case just "Buy" Steam from the Software Center and install it fresh.
To the other part of the question. Ubuntu One is a cloud service but it is also part of the "Single Sign on" that allows you to sign in across multiple Ubuntu related sites as well as Ubuntu One's cloud service. In this case it is used to sign into the subscription record of your account so that you can reinstall the "purchased" software without buying it again. If you have never used it then just create an account via the link in the upper right of the page and then you can install Steam.