You ever notice you don't see those types of image tricks done on REAL websites? Google? Amazon? E-Bay? IMDB? Wikipedia? Slashdot? These forums? You may wish to reflect on that as there's a VERY good question you may want to ask.
Is there a REASON "real sites" don't do that?
It sounds to me like you've backed yourself into a corner with a classic "Doctor, doctor, it hurts when I do this." -- you're using images that are causing problems -- solution? don't use a image, or remove the image with media queries where it doesn't do what you want. You could even swap it for a different one -- maybe, usually on small mobile displays photograph type images look like crap behind text anyways!
There is also the new CSS3 background-size option.
You want it to stretch to height preserving aspect ratio, you do:
Stretch to width aspect preserving:
stretch to fit, to hell with aspect:
You can also use:
To make it so that it always fits height or width as needed.
Though, it also sounds like you are using presentational markup instead of using padding and margins... since your first part sounds like what should be a H1 with a SMALL tag inside it (master heading under which all other headings are subsections, which is why you should only have one H1, SMALL providing de-emphasis on the tag-line -- YES, small has a semantic meaning too). If it's JUST a tagline, and it's NOT starting a new subsection of the page, it has NO business in a H2.
While common practice this:
Is gibberish made up by people who never learned what a heading tag is, what heading levels MEAN, or how to use HTML properly. See the idiotic "HGROUP" tag from HTML 5, that was FINALLY stricken from it. Now if we can just get SECTION, NAV, ASIDE and FOOTER stricken as redundant to numbered headings and horizontal rules...
In any case, you should concentrate on semantic markup FIRST, then bend that markup to your will with CSS. Adding a tag that has a semantic meaning -- like P -- to your markup JUST to create a gap between elements is... well... There's a saying I use a lot:
"If you are choosing your tags based on their default appearance, you are choosing the wrong tags for alll the wrong reasons!"
Though really to weigh in properly on this, it would really help if we could see the site (live and it's code) in action.