I'm about the last person that anyone would accuse of being an artist, but I'll attempt something of a response here.
In terms of bringing something to the world, and of overcoming obstacles and avoiding distractions, I would say that I am rather emotional person, that I try to see and meet people where they are at, and that I try to keep things open and emotionally honest. I've heard this notion several places, but "leave things better than you found them, and if thats not situationally possible at least try not to make things worse" is pretty good general advice, particularly when dealing with other people.
4's can be VERY moody people [goodness help us all!] but it also gives us an incredible ability to see into others, see what makes them tick, see what is bothering them, and to help them "process their stuff."
For me, giving manifestation of my skills and interests [which I'm pretty sure no one has ever called art!] is about helping other people understand at least part of their inner world and helping them to process stuff and to "heal" emotionally, mentally, spiritually, or however.
I think your ?motto? [really, what is that called? tag line???] about "repurposing anger" is very interesting. I've had multiple spiritual healers point out that "Buddhists* are experts at transmuting negative emotions into positive ones", and I immediately thought of that when I read your motto/tagline/whatever. I don't want to turn this into a teaching Buddhism* post, but I would suggest to you that if might behoove you to look into how the Buddhists* [and others] do such things. I'm not sure how helpful anything I would have to say personally on this matter would be [I'm definitely not without experience on this matter], but I could try if you wanted me to.
Various thoughts from my past somewhat relating to "repurposing anger":
-I can't pick or control what other people do, but I can still make my own choices.
-I am strong enough in character that even though you treated me the way you did instead of reflexively reacting I will process this and make a decision coming from both wisdom and compassion.
-The consequences of their actions have already been set, but my consequences have not. Choose wisely.
-IN this moment, right here right now, what will you create? What will you generate? What "legacy" will you leave behind you?
-What kind of person do you want to be? They did what they did, but don't respond negatively and become a lesser moral person for it.
-Choose joy
-Choose happiness
-choose meaning
-choose value
-choose a life worth living
-if the situation were reversed what do you wish they would do?
-be happy and share your joy
-try to leave things better than you found them. if that simply not situationally possible at least try not to make it worse.
-if absolutely nothing else try to bring more "awareness" to a situation.
I guess none of the above are really "repurposing" anger so much as making conscious deliberate choices and hoping to be wise about them. Transmutation or repurposing is a much more involved matter&. I would say that, to do it well, requires much more developed abilities with subtle energies and particularly with the anahata chakra. To simply ignore anger, and make a positive constructive choice is definitely easier to pull off.
*declaration 1: I have significant background in Buddhism, including transmuting negative emotions.
& declaration 2: I also have background in tantra, which takes transmutation to a whole other far deeper level.
I remember reading, in a book on shamanism I believe, that compassion, compassion was the right word here right?, literally means "shared suffering." Some people can be healers without having experienced pain themselves. Most healers need to have experienced pain or suffering themself first. Healing can take many forms or methods of expression.
"They use their pain and other intense emotions and transform that into something beautiful, something to share with the world." "What does it take to block out those negative, sabotaging thoughts of being broken and truly be inspired and fearless in your mission?" "In short, how do you rise as a phoenix from the ashes of your pain?"
No one is perfect. We all have pain in our background somewhere somehow. Many people feel, at least somewhat, like some part of themself somewhere somehow is broken. One answer is that we all get up from where we are, dust ourselves off, and start moving forward. When we deal with others, we often see how much more difficulty or pain or brokenness that they have than we do, and that [hopefully] motivates us to let go off or at least place less importance on whatever brokenness we may feel inside. Nobody is perfect at everything. Many people are greatful for anothers attention, for anothers goodwil, for anothers "trying" even if our trying didnt actually concretely do very much.
At the end of the day, we all live our lives make decisions and face their consequences. Don't expect that you will be perfect and don't expect that others will expect you to be perfect. Do the best you can, be grateful for what you have, find joy where you can, be happy and share your joy if you can, and know that everyone has problems and we are basically all in the same boat.
Does any of that address your questions? Were you looking for something more art-centric? Do I get INFP-healer brownie points for all of this?
Good luck with repurposing your anger. Anger can motivate people to accomplish things they otherwise wouldn't be able/willing to do. That can be either good or bad depending on the situation. Anger also poisons the one who feels it. It's your life, to the extent that you can make decisions that will serve you well.