It sounds like you're happy with your rankings and aren't quite sure why you have them. You're right to be careful.
Once upon a time, many years ago, the combination of keywords in anchor-text, title, and headings was sufficient for ranking. Before CSS, the H1 heading was the big bold text at the top of the page. Since the algorithm tried to emulate human perception, search engines naturally assumed that big bold text suggested the topic of the page. Additionally, the use of headings... h1, h2, h3... gave the page something of a hierarchical outline structure, with the main topic (in h1) at the top.
CSS has enabled modifying the appearance of headings while preserving their structural nature. The h1 tag, though, over the years, has been so misused that the search engines have paid less and less attention to it. Some testing reports that the h1 tag itself no longer has effect on rankings. I've continued to assume that it doesn't hurt to have a classically well-structured page, though it's sometimes best to be subtle about it. I certainly wouldn't yank a relevant main heading from the top of a ranking page and replace it with a graphic.
It's likely that your page has come to rank because of factors beyond your initial structure, but you don't know what those are. I haven't seen a ranking page with a large unformatted h1 heading for quite some time. I'd modify the appearance of the h1, as tangor suggests, with CSS to make it more attractive, but otherwise keep it looking like a heading... primarily for the user.
Since you're not completely sure why else you're ranking, I'd keep the key text elements all the same. Changing the appearance of the page with CSS styling, though, shouldn't hurt at all, and in fact it's likely to help. Ditto with adding attractive images, so long as they don't greatly slow down the loading of the page. But keep text as text, and headings as headings.
One other factor to pay attention to... I've seen some webmasters assume that navigation doesn't matter much, and that's where I've seen redesigns come back to bite them. Site structure and navigation anchor text is extremely important. If you're not sure what you're doing, it's hard to give general advice beyond that, except to hang onto what works, and make other changes slowly, after your redesign, when you can check them out individually. If you make a lot of changes all at once, you won't have a clue what went wrong.
