You are still getting caught up in conflating the quality of something specific that is produced with the underlying processes that give rise to that act, some of which may be tied to "general intelligence". Let's put aside "creativity" for moment. Building a house by yourself without prior training is not "an example of general intelligence", but it would be heavily aided by greater general intelligence.
There are many problems to be solved and most of them have objectively right or wrong answers as whether the house falls down will attest to. Figuring out both what you need to do and more effective means to do it would be impacted by general intelligence. However, imagine that you had 10 years of training as a furniture maker. Those trained skills and knowledge now come into play and help you make those decisions and execute them, thus somewhat reducing your need to rely upon your general intelligence to do the same things. Also, if you have better hand-eye-coordination, your work will be of higher quality and that influence is separate from the impact of your general intelligence.
I am the writer in the family. My sister is the artist. My brother is the inventor. All three of us sing quite well and my brother and I both studied musical instruments, he the guitar and I the piano, oboe, and saxophone.
My sister and I were excellent students, my borther not so much but he excelled at strategic and design thinking, I can't draw a straight line and my sister while compotent at writing, will freely tell you her prose and poetry leave much to be deserved if you are looking for a WOW factor.
So, "creativity" is a fuzzy and messy concept, in large part because so much of what we call "creative" has no objective criteria as to what is better. There is no end-state to be reached or particular problem to be solved, unlike building a house where there are many objective metrics by which to judge its quality and whether it solves various problems that engineers worry about. IQ has strong association with controlling attention and processing information in relation to some desired outcome or goal. This isn't esoteric to school. We do such things all the time in daily life. However, many things we categorize as "creative" don't have that property. IOW, there is no real utility or functionality to creative works beyond a vague notion of causing an emotional response in others. I'm not devaluing art, just saying its value isn't in its problem-solving utility. If there is no particular goal, then there is no need to control attention and processing towards serving that goal. A meandering, unfocused mind (or drug induced one) can produce as or more creative things than the focused one. Thus, theoretically, IQ shouldn't relate to things like how artistically creative what you produce is, and empirically it is not related to this.
Writing isn't all about "creativity" either. The more that the writing has an a priori goal and restrictions on it, the more it is problem solving and the less simple creative novelty. Prose to convey accurate understanding of evolution is less "creative" and more influenced by general intelligence than poetry. Take a science passage and just cut it in half. One will be objectively better than the other, meaning better meets the goal of accurately describing the phenomena. Take a poem in cut it half, and which is better? Does the question even mean anything? Would people agree which is better? Is cutting a finished poem in half a creative artistic act itself, thus making that one better? As a rule of thumb, if the the thing being produced cannot be rather reliably measured in terms of objectively better at meeting a specified goal, then IQ isn't all that relevant to it.
Music is even more complicated because isn't all about creativity. Creating versus executing music are completely different and likely rely on very different causal influences, with executing music relying more upon things related to general intelligence like memory and being able to divide attention between executing the current bar while thinking about what is coming. Not to mention, music requires physical skills that are unrelated to the information processing that underlies general intelligence. One reason some people are better at instruments than other is as simple as the length and shape of their fingers, or even how their fingernails are attached. My nails are attached at the very tip of my finger. No matter how short I cut them, I cannot press on a surface with my fingertip without my nail hitting and preventing me from getting even pressure over the area of my finger tip. The greatly inhibits my guitar playing. I cannot get good pressure on the string in order to get a clean sound.
Do our weaknesses average out with our strengths to come up with a general intelligence?
No. You are using "general" to be "averaged across all things". That isn't what the general refers to. It refers to the fact that there are some aspects of information processing that are so basic that they have a general influence across tasks that require learning new things.
Our is the idea of a single measure misguided and prone to misuse and perhaps a better stance is multiple intelligences or what the old folks always called talent?
Again, no one says that general intelligence is the single measure of all things important for human performance of all types. Lets use an analogy to physical activities. Lung efficiency is to sustained physical performance what general intelligence is to cognitive performance. It impacts most kinds of relevant performance to some degree (thus is general) but it isn't everything that impacts those performances and differences in it can be made up for by opposing differences in other things. However, since differences in those other things are just as likely to be in the same direction as in the opposite direction of IQ (or lung capacity) differences, most of the time the person with greater IQ (or greater lung capacity) will outperform any randomly compared person.