Hoping to get a spark,
First, I am a huge proponent of the "becoming friends first" method of dating. It's a great way to find out if you're compatible, if you communicate well, and if you're genuinely interested in who each other are. The only downside is transitioning out of the zone where you now find yourself.
Unfortunately, there's no standard fix for this. We are given three main options in every difficult situation we're faced with (although, they can be used in various degrees and combinations): change our perspective of it to realize it's not so bad, attempt to constructively alter it in a way that makes us happy, or lastly, get out of it. Notice how none of these options include changing how other people think or feel? Yeah, I know, it's a bummer.
For you and Julie, the first option means remaining "just friends." This is certainly the easiest choice, but it can be masochistic as it often means watching as she falls in and out of love with other people and likely sacrifice your own shot at a fulfilling relationship. However, good friends are hard to find, so it's time to be truly honest with yourself. How much are you willing to sacrifice as you wait for her to feel the spark too? Do you think you could find another woman when you're spending so much time with Julie? Do you think you'll be ok when she finds someone else? You're the only one who can truly assess how painful this friendship will be for you in the long run.
The second choice (altering the situation) suggests that you let her know how you feel about her and that you'd like to take it to the next level. I'm all for the direct approach, but creating more romantic settings and flirting can provide hints without being so confrontational. If you make yourself unambiguously clear and she's still unsure, then give her time to think about it. And BTW calling or texting every half hour with "do you like me now?" will likely not help her figure it out or make her more attracted to you.
Which leads us to the last option: pull back. This can achieve two things. First, begin the "getting over" process, and two, it may allow her the chance to "want" you. If you're always around to answer the call, text, or to hang out, she may take you and your friendship for granted. Romantic relationships are built on love (giving) and passion (wanting). Let her "want" you. Often times, women are less likely to be attracted to men that follow them around like lost puppies and prefer independent types.
Now, remember that part where I said we can't change the way people think or feel? I still mean that, and attempts to do so are manipulative. Games are not good, which is why I'm not suggesting that you sit alone in your room waiting for your phone to ring so you can not answer it. Rather, be sure that you have your own life outside of her--rediscover healthy habits, find new friends, start up a hobby, just find ways to keep busy without Julie.
In all truthfulness, if distancing yourself results simply in more distance, moving on may be the right thing to do. It does not make sense for two single heterosexuals of the opposite sex to hang out so much that other people think they're together. It prevents both of you from finding a more wholly fulfilling relationship by allowing you to settle for a pseudo-romantic friendship, and deters other partner-potentials around you from showing interest.
The friend zone can be a fun or an icky place to be. So, Flint, you can find a new appreciation for it, discover if she views it as a more-than-friend zone, or get the heck out of there. It seems like you're a caring and decent guy looking for more than a random hook-up, you deserve sparks, so don't settle for less.