Watching your toddler make extra messes to clean can be frustrating... and with the addition of a new baby to care for, I'm sure that the last thing you want to be doing is cleaning up an extra food mess.... I empathize with your annoyance!
The mind thinks in pictures... so when we tell a child not to do something, such as don't (throw your food), the picture that appears in his mind is throwing food... and the child then has to figure out what to do instead. A simple cooperation tool that I learned, is to tell the child what TO do instead of what not to do (in this case "Keep Your Food On Your Tray")... This way, you are offering the child the image of the positive behavior you want him/her to see and do.
Another thing you might try would be to acknowledge the child's perspective
"I know that throwing things can be fun"... then offer info, "But Food is for Eating"...
and offer an acceptable substitute to meet his desire....
"a BALL is for throwing.... as soon as we're done eating, we can throw the ball together"
(perhaps getting some of those "crazy balls" often found in gumball-type machines - the kind that bounce really high - to drop off his high chair tray during a non-eating time might be a fun and positive way for him to meet his playful desire (***ONLY under close supervision, though, since their small size could present a choking hazard***) then if the child begins to throw food, you could remind that food is for eating~balls are for throwing... as soon as you're done eating, we can play the ball-bouncing game.)
If you think the reason for his food throwing behavior is because he is done and bored with eating... then you might try teaching him skills for signaling that he is finished/letting you know that he is done. You could tell him...
"Food needs to stay on the tray - if you are finished eating you can say "all done"
(or you could offer him a hand signal he could use to show that he is "all done")
IF the behavior is intentional, with a goal of attention/involvement, then continuing to correct more than once, will give the behavior a payoff and continue the attention cycle.
An effective way to break a negative attention cycle is to respond ONCE, offering the child an acceptable way to get your attention, then ignore.
You might say something like...
"I can see that you want to play.... but throwing food makes a big mess that mommy does
not want to clean... If you want me to play with you, you can ask me - like this, "Mommy will you play with me?" (or if your child is not yet that verbal, you could offer a hand signal for him to use that means "I want you to play with me")
Ignore the behavior (not responding verbally or with your body language), until the child displays the appropriate behavior that you want to see. As soon as he does, reinforce with descriptive, encouraging statements that describe the positive behavior and the value of it.... such as "You asked me to play with words (or with our special hand signal) this time!... I'm glad to play when people ask with words/signals.......... and look, you kept your food on your tray... right where it belongs... now there is less time to clean and more time to play..."
Throwing food is a typical toddler behavior that many parents struggle with and I agree with your recognition that this behavior is probably at least partly caused by the child's developmental stage of exploring and developing independence... Sometimes, though,
(and this may or may not be the case in your situation) the way we respond can cause unintentional, developmentally appropriate behavior to mutate into deliberate misbehavior with a certain goal.
I would begin with the assumption that the behavior is unintentional and try inviting cooperation by using tools like positive requests, substitution, etc.. and by teaching skills...
If the behavior is intentional, your child will probably go out of his way to show you this, and then you can respond by attempting to break the attention cycle by offering him a more positive way to get your attention, and ignoring until he displays the behavior you want.
Keeping in mind the long-term result you want can help, as you try to ignore the behavior (also prevention-wise, putting smaller amounts of food on the tray... ie.. only a few bites at a time... then adding more as it is eaten can help avoid a big mess to clean)...
If the goal of the behavior is truly attention/involvement then it seems that it would logically follow that getting zero attention would cause the behavior to stop after a few unsuccessful attempts.
If the behavior continues (after consistently trying this for a few days) then perhaps, there is a different goal.
Hope these suggestions help!
I'm sure that with your own experimentation and the many different suggestions you receive, you will find what works for you and your child.
Good Luck!
S.