My overall advice: If something is not working in your routine, then adjust the routine. Much easier to adjust the routine than to adjust the toddler!
My daughter Jillian is also almost 3yo (and fortunately doesn't do many tantrums), so I don't have much advice on how to stop that habit (sorry!)... However, I wanted to mention that I've noticed a certain 'romanticism' that she has for being "Baby Jillian". Now, it doesn't come out at the table (like wanting to bed fed)... However she does insist that she's a baby (or refers to herself as Baby Jillian) on our way home from school, after bath and before bed. She'll even go so far as to insist that she is not a big girl (and will get quite worked up about it!) if such a comment is made during her Baby Jillian mindset.
So, I really think your daughter's 'baby behavior' is a phase... Just part of the normal independence phase, then clingy, then independence, etc., as well as testing limits and seeing what she can achieve through her behavior. The problem is, the more you refuse her some 'baby time', the more anxiety it produces in her.
A few months ago, my daughter was clingy (although I wouldn't call it tantrums) and preferred me over my husband in the mornings.. So, I had to wake up earlier and be totally ready before she woke up. For whatever reason, she needed more 1-on-1 mama-time (sitting next to her watching Handy Manny!) in the mornings before daycare. It was a 6 week phase.
I would stop feeding her yourself. If she doesn't want to use a fork or spoon, then just let her eat breakfast with fingers. Also, my daughter drinks a big yogurt smoothie (which she is excited to drink with a colored straw she picks out) as soon as she wakes up (when she's too groggy to argue), so if she doesn't eat much of her actual breakfast meal before school, at least she's got 1 to 1.5 cups of yogurt in her belly...
My other suggestion... Does she have a favorite baby doll? As in one that she can baby? My daughter has a couple plastic babies, however she really wanted one that would cry for her. So I traded her Halloween candy for a new baby doll which cries and wiggles (not the full-blown Baby Alive though). I must say, that it has helped funnel some of that "take care of Baby Jillian" mindset towards "taking care of her baby". The babydoll was $14 at Target and goes by the brand Mommy & me (and has an on-off switch!). She may respond to the idea of feed her baby at the table while she feeds herself... Just and idea.