How to calculate stock+FX gains in a foreign country?

I'm curious about how taxes work, and through my accountant+this forum I've learned a bit but that only opened more questions. So I'd like to ask with a practical example. This is all about how to calculate the gains:

1. Let's say I start with 100k JPY, and at the starting date the exchange rate is 1:100 (EUR, but doesn't really matter). I transfer it to my country in EUR, so I get 1,000 EUR in my bank.
2. Few months later, when the EUR:JPY is at 1:110, I invest it into a ETF, a fund, etc. This is still 1,000 EUR invested though.
3. Then a couple of years later I've done very well and those investments are valued at 2,000 EUR, so I decide to sell. At that moment, the EUR:JPY is at 1:150.
4. Finally, a few months later I decide to send the 2,000EUR back to Japan, and then the rate is at 1:160. So I get 320,000JPY.

When I sell in step [3], AFAIK the gains are "Sell time value in JPY" – "Buy time value in JPY", so this would be (2,000 * 150 – 1,000 * 110) = 190k. Then Japan taxes are calculated on that. This seems to imply to account for both stock and FX gains/losses during that period.

So then in the last step, I'm not sure how to calculate the gains. This is because:

• If we use the initial value of the JPY transfer there's two problems: we are calculating JPY gains twice, and I understand that you only have to pay taxes once for a given gain. Also, initially we only had 1,000 EUR and finally 2,000 EUR, so 320k-100k JPY would also not work for gains, it'd either have to be 160k-100k or 320k-200k.
• We could use the 4 "events", meaning (320k [4] – (2k*150) [3]) + (1k*110 [2] – 1k*100 [1]) = gains. But what happens if I already had money in my country? And do I need to keep track of the EUR buying price potentially for decades? That feels a bit absurd (and if I've done something like cost averaging where every month I buy stock, it'd makes things absurdly tricky to track).

Alternatively (though I am 99% the answer is "no"), can I instead on step 3 declare the gains as "EUR profit – EUR cost" => JPY (at the sale time)? That would make things so much easier, and it feels weird that I have to bake in the FX gains within the stock trading when I'm not doing any conversion.

(notes: yes, I'm a Japan tax resident, 5+ years here. I'll also ask my accountant this question, but wanted to know Reddit's take as well. All numbers are made up for simplicity and privacy)