Basement supporting wall header increase
What state are you in? You should check out the span tables for your local code. Generally, for that span outlined in the drawings above, you should be safe with triple 2 x 12s, providing you use grade no. 1 lumber. A less conservative header size might be possible, though. A laminated beam is also a valid option. These codes take climate and real life loads into consideration and they are generally VERY conservative -- for good reason.

Here are example span tables, see page 2:

http://www.southernpine.com/media/SS_7-12L.pdf

Also, I see you only have one jack stud on each side of the header. There really should be two.