I really wouldn't recommend the Love and Logic thing with a child who is already totally in control. That's more of a program on how to give her even more choices and giving yourself ways to think of all different reactions to her tirades while re-adjusting your own thinking rather than NIPPING THE DISRESPECT, TANTRUMS AND ACTING OUT. Love and Logic is a good guideline for having a loving logical house in general, but it has no discipline. All my friends who used that program, had very bratty kids.
Time outs: Do not phase spirited kids, and as you have seen they enable tantrums like crazy.
Taking privileges away: Correct, not immediate enough, and in the privileged world our kids live in, losing a few luxuries they didn't earn is a far cry form a serious consequence, since they still have lots of nice things.
The occasional pop on the butt: Does nothing at this age. It would have done wonders if used consistently at age 1, to prevent the terrible twos, and would have continued to work well through the 2's if consistent enough. Ideally she would have phased out of spanking by now and cared about other consequences, but her foundation didn't stick for whatever reason.
So. Here is maximum discipline for a 5 year old gone awry (after a calm explanation of her behavior and warning at first, so she gets it before you follow through. this will cut down on the amount of times you follow through, but you WILL have to follow through, because she won't believe you just telling her.) It needs to be consistent for all things (after a warning) so she understands that NONE of the different behaviors: tantrums, making faces at you, screaming at you, throwing things, telling you no, refusing to eat, going limp, etc etc etc, are allowed. You want ALL this bad behavior to stop NOW. Do not listen to Love and Logic telling you to do all different nice creative things as reactions to each different thing she does. NIGHTMARE results.
First, start by telling her that from now on she will not be allowed to do x, x, x, and x. You will not yell, you will not warn her twice. She will get a serious spanking (this could be as many as 5 hard swats on the butt for 5 years old-I know it sounds harsh, but this has escalated and wasn't prevented), and THEN she will ALSO be removed from any nice activity she is doing (technically a time out, but at least she had a consequence first) and while she is there crying from her spanking (not having her own spastic cry fest for no reason-and if she's "not crying" to show you she "didn't care"-all the better) you will ALSO take _____(insert favorite item) and put it away for a week. ALSO, she must DO something like a difficult chore that she would not normally have to to do. (make a list of chores she can do so when the time comes, you're ready) ALSO she must EARN back the favorite item with a week of good behavior, or she doesnt' get it back.
ALL OF THIS. Every time. For EVERY THING. It didn't have to come to this, but it has. I admit, I have not had to go these lengths with my 3 kids, but I was this diligent within their age ranges from age 1, so now at 3 and 5 my oldest 2 don't ever try this kind of stuff. But this is what I would do in your case.
Let's take tantrums: You see the FIRST SIGN of tantrum. She gets one CALM warning not to begin it. She decides to proceed. Do the above ENTIRE sequence. If she tries to escalate the tantrum after a few minutes of normal crying, she gets another warning, and a repeat.
Next tantrum, same thing. You may not stop a current tantrum in it's tracks, but she will eventually choose not to have them knowing what will definitely happen.
She tries to make a face at you: Warning (first time only), then same thing if she proceeds.
She throws things: Warning (first time only), then same thing if she proceeds.
After she has been warned for something, at 5, you can just enforce with no warning for following times at the same things since she will understand and remember what she's allowed to do. But give the first warning, for the sake of teaching her to follow warnings.
It seems like an out of control overboard consequence, but soon you won't need it anymore. In public, if you can't enforce, she is old enough to have her consequence when you get home. Never skip it. And to be honest, you probably don't need 5 swats if a swat or two stings enough. I've never needed more than one with my kids, but there are some super difficult kids in my family (boys) that occasionally needed a few swats. The key is acting immediately, firmly, and always.
Never get mad, never yell. You are showing that your reaction is because of her choice, not your anger. Always give her a chance to stop the wrong action, and make the right choice. She never should have been allowed to carry on a tantrum that long without intervention. That will make this a very hard habit to break, but it can be done.
You will see her turn around QUICK. And you'll see her growing much happier as her behavior improves and your relationship will blossom. Kudos to you doing it on your own. My husband is always gone and I do this with my 3 and they are all well behaved. It's was a lot of work at first, but now all the fun we have and their self pride made it worth it. You can do it. I've seen difficult kids of divorce turn around when people stepped up and started enforcing firm rules this way. If your fiance is really going to be her dad, he needs to be right there on the same page with you, not the good cop, and this will go twice as fast. As your relationship is now though, I'm not sure you feel comfortable letting him discipline her, that's your call. A united front is always strongest if he is trust worthy.
Don't forget to spend extra loving close time with her in general. Her wanting to have your respect because she loves you is part of the big picture.
If you firm up this much within a happy loving home, and see no improvement, yo can take her to the doctor for evaluation with a clear conscience.
Oh, and for the not eating, one chance to eat, or nothing until next meal. I wouldn't enforce the rest of the discipline for that or force her to eat. But I would enforce good table manners.