Is there any way I can achieve my goal without having access to my .php files?

Indeed.

It looks like you have a good start with the custom CSS you've saved already. What you'll want to do is make the #site-title height big enough but set the background and spacing for the link inside #site-title as well. The "a" element (the link) is the clickable part, so that's why you want to set the width and height values for that one.

I see this in your custom CSS right now:

#site-title {
	background: url('http://edwardsflorist.files.wordpress.com/2013/02/final-edwards-logo-copy-60-smaller.png') no-repeat scroll 0 0 transparent;
	height:252px;
	width:480px;
	display:block;
	margin-left:auto;
	margin-right:auto;
}

Try changing "#site-title" to "#site-title a" and adding this:

#site-title {
	height:252px;
}

I am pretty sure I'd be able to do this if I had access to the theme directory files, but I am working off of a free blog (with purchased custom design upgrade), so I only have access to the .CSS file. Is there any way I can achieve my goal without having access to my .php files?