Thanks for the information folks. Due to my inexperience with php and css, I went for the quick hack by changing this:
<input type="submit" name="mc_signup_submit" id="mc_signup_submit" value="<?php echo esc_attr(get_option('mc_submit_text')); ?>" class="button" />
To this:
<input type="image" name="mc_signup_submit" img src="<?php echo get_option('home'); ?>/wp-content/uploads/res/Signup.png" width="99px" height="50px" alt="Sign Up!" class="button" />
I could probably replace the alt string with the old code to get mc_submit_text, but I’m not too concerned right now.
This gives me the ability to upload a new image without changing the code, but I’d need to update the code if I change the size as well as every time that this plugin is updated. That’s ok with me as I’m happy to use all the rest of the hard work on this plugin without this one sticking point causing me problems.