Y.M.
My kids enjoyed throwing food too. They would throw it when they were hungry and when they weren't hungry. My youngest also loved to throw her dish on the floor when she was done almost every time.
This is what I did:
My son... has been through a lot... cancer treatment and chemo. He was on a G-tube for a while. As he was learning to eat by mouth again, I couldn't risk him missing meals or calories because he wanted to play in his food, throw it, or even be a little bit naughty in his behavior with it (purposeful messing). I had to tolerate his messing with the food and even being naughty because he would still continue to take a bite every now and then while messing around. It was at this time of crossing over to solid food from G-tube feeds that I introduced play dough. He needed to mess, throw, and mash food (dough) for developmental purposes. I had him play with play-dough at times when he was already fed, had sipped a bottle of milk, or had a full belly, so that his developmental need alone would be met just with the play dough time. Then, when I placed the food infront of him, at a later time, I would tell him that the playdough is for mashing but the food is for eating only. I encouraged him to only take bites of the food, I tolerated a lot of teasing and taunting on his part. And I was a little flexible with my boundaries because I didn't want to spiral him into a tantrum when it was so important for him to just become engaged in the eating process.
The two activities (between the play dough time and food time) didn't connect or come together for a long time, but eventually he knew what I was going to say, how I was going to strongly direct and guide him to only eat his food, and how I would set aside time for mashing, rolling, and throwing the playdough. Somewhere along the line, his brain got the connection and his needs were met. His desire to mess with food lessened more and more. Eventually he began eating automatically with no prompting at all to become engaged with picking the food up and placing it in his mouth one bite after the next with no messing around.
My daughter though... she didn't have an eating problem at all. She's always be a thick little healthy chunk. I had no problem at all with swift consequences when it came to her. I did the two chance rule with no worries most of the time.
During the meal time, she would receive forgiveness of messing with the food two times, and then I'd take the food away. There was only a short period of time where she messed with the food even when she was hungry and she threw her plates on the floor even if she was starving. She struggled a little and would beg for milk bottles or sippy cups when she missed a meal because of her behavior. At first, I gave her the bottles, but eventually lost sympathy for that as well. She would be hungry, fussy, sleepy.... just miserable. But, when food was placed in front of her, she'd throw it down and smash it and mess it again. I was not concerned for her health though so I just let her go through a little misery. I believe that by letting her be a little hungry, she actually learned quicker.
With my son, I just couldn't take the risk. It was more important to get him engaged in eating than it was for me to be "teaching lessons". But, with both children, even though it may not make sense at all... the whole food throwing and mashing thing had very much to do with a developmental phase that they needed to meet. So, I would introduce activities like play dough (preferrably home made), longer baths with more water play, more snuggly pillow time (just to roll and snuggle in the pillows with only a diaper on). Snuggly pillow time will meet a lot of sensory needs. You'll find that as you introduce those other sensory/developmental experiences into the day, the outpouring of attention on the food will lesson because the need is being met elsewhere. Eventually the brain makes the connection. However, it does take a while.
Each child is different and should be given a different kind of tolerance when it comes to this issue of food and fingers.