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Yes. But it requires proper attention. Since you mention "fun", let's first look at pleasant rebirths:
DN33:1.10.94: Three kinds of pleasant rebirth.
DN33:1.10.95: There are sentient beings who, having repeatedly given rise to it, dwell in pleasure. Namely, the gods of Brahmā’s Host. This is the first pleasant rebirth. There are sentient beings who are drenched, steeped, filled, and soaked with pleasure. Every so often they feel inspired to exclaim: ‘Oh, what bliss! Oh, what bliss!’ Namely, the gods of streaming radiance. This is the second pleasant rebirth. There are sentient beings who are drenched, steeped, filled, and soaked with pleasure. Since they’re truly content, they experience pleasure. Namely, the gods replete with glory.
In the same sutta, Sariputta explains that ethics and view affect rebirth:
DN33:2.1.35: It is because of endowment with ethics or view that sentient beings, when their body breaks up, after death, are reborn in a good place, a heavenly realm.
Ethics affect the quality of rebirth (e.g. good place or bad place). However it is view that most affects rebirth itself. In particular, we have to examine our view, since a vital condition for rebirth is a view conditioned with continued existence and grasping:
SN12.23:4.6: I say that rebirth has a vital condition. And what is it? You should say: ‘Continued existence.’ I say that continued existence has a vital condition. And what is it? You should say: ‘Grasping.’
Meditation allows us to change our conditioning. It allows us to let go. So if we are ethical and meditate well, we might see and experience the wisdom of non-return and beyond.
DN33:3.1.105: The heart’s wish of an ethical person succeeds because of their purity.
A person shouldn't worry about "too much good kamma" or coming back as a human. A good person with much good kamma should consider why they wish to come back at all.
MN1:171.4: Because he has understood that relishing is the root of suffering,
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From Awareness Itself by Ajaan Fuang Jotiko, compiled by his disciple Thanissaro Bhikkhu:
A group of laypeople who had studied the Abhidhamma together came to Ajaan Fuang to try out his version of mental training, but when he told them to sit, close their eyes, and focus on the breath, they immediately backed off, saying that they didn't want to practice concentration, for fear that they'd get stuck on jhana and end up being reborn in the Brahma worlds. He responded, "What's there to be afraid of? Even non-returners are reborn in the Brahma worlds. At any rate, being reborn in the Brahma worlds is better than being reborn as a dog."
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Can a person choose to reincarnate as a human instead of a god?
Well, if by "choosing" you mean one can pick and choose out of 2 choices given to you, then no. But if "choosing" means to cultivate the Dhamma in both merits-making and wisdom, one can affect/influence the future course of one's rebirths, then yes, definitely. Most of the cases when one's acquired tremendous worldly merits either here on earth or up in the heavens was because they solely focus on the merit-making part, while paying little to no attention to the cultivation of Sila/Samadhi/Panna.