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My math is exactly correct. Note the assumptions "for any reasonably-sized constituency" and "if the votes are evenly split among districts." That's the very well-known mathematical practice of freezing or bounding certain variables in order to focus on the effect of others.
Let's say a reasonably-sized constituency has more than a few hundred voters. Then the anomalies you'd see with 1-person districts won't happen. First simplifying assumption.
In that scenario, with votes evenly distributed, 50.1% for Party A in each district leads to Party A controlling 100% of the seats, as I said. And if there are more than two parties, as long as the vote is evenly split among districts and Party A is the leading party, Party A will still get 100% of the seats. You can keep arbitrarily adding parties to show the same effect with even smaller vote shares.
Your observation that even smaller vote shares can still control a legislature is correct, but requires multiple parties with roughly similar vote shares, or votes to be distributed unevenly to the parties among the districts. That's a bit closer to how real elections work, but in practice, most uneven distributions cancel out each other's effects, and only relatively few of such patterns can lead to the extreme cases you describe. And there are seldom many parties that gain over 10% of the vote. Those things can happen, but it's putting you a few sigma out on the tail of the curve. Though in the UK, recent governments have had parliamentary majorites won by parties that got 35-40% of the vote. FPTP with multiple parties can cause that. Changing constituency sizes wouldn't have any effect on that kind of outcome.
Your match is correct to get 100% of the districts, but a party only needs to get between 50 and 75% of the seats to have uncontested control of the legislative body, depending on their particular laws, meaning that above that threshold the rest are poorly represented, if at all. Hence, as little as 25% of the popular vote, even with only 2 parties. Yes, without perfect gerrymandering, you won't reach those numbers, but minimums and maximums don't care about sigmas.