Hi Neil,
To the best of my knowledge, using an <h> tag will always put a break before the copy.
I suggest using a <div class="blah">copy</div>. You can also use the class within a span, p or table tag. This should fix your problem.
As for the search engines, what you are saying used to be true but I am not sure it is still the case. I will ask some of my search engines bud***s and get back with you.
Thanks,
Allen