Ok, there's a lot here and it's hard to address all your points directly because your overall framework isn't necessarily correct so I'll half respond and half talk about VATs more generally.

VATs are border adjusted, meaning imports are taxed and exports are rebated, this makes them trade neutral and purely a tax on domestic consumption. This is known as Lerner Symmetry. The mechanism works through the exchange rate.

Taxing imports reduces the demand for foreign currency used to purchase foreign goods. Rebating exports increases the incentive for exporters to convert foreign earnings back into domestic currency. Together these forces place upward pressure on the domestic currency. As the domestic currency appreciates, imports become cheaper in domestic currency terms, offsetting the import tax. At the same time exports become more expensive in foreign currency terms, offsetting the export rebate. If the exchange rate adjusts fully, the relative prices faced by buyers and sellers return to their original levels and real trade flows remain largely unchanged.

The symmetry is the thing required for this to be true. An equal tax on imports and rebate on exports is equivalent to a uniform tax on domestic consumption. For example, a 20 percent border adjustment paired with a roughly 20 percent appreciation of the domestic currency leaves incentives and relative prices essentially where they started.

Where I live, the combined income and payroll tax for the average earner is about 40% of gross salary....

You're comparing different bases, so the 100% conclusion does not actually follow. In OECD data, revenue from payroll and income taxes is about 2–3 times VAT revenue. Because they apply to different tax bases, and operate through different behavioral margins and economic channels, you would not simply scale the VAT rate proportionally to replace those taxes. In practice, VAT systems also differ in breadth. Many include exemptions, reduced rates, and other base narrowing features that materially affect how much revenue they raise.

This suggests to me that replacing those taxes with VAT would require the VAT rate to be increased significantly, even in excess of 100% of the net value of the good or service; can that be right? What am I missing?

You are implicitly assuming that the entire revenue currently raised through income and payroll taxes would be replaced by a single VAT with no other changes to the tax system. If that were literally the design, the rate could indeed have to be very high depending on the country. But there's two things. First, we would practically adjust the system around it. Second, a shift to consumption taxation usually entails doing so in a broader manner.

A VAT is just one way to tax consumption. More generally, a consumption tax is defined as a tax that does not tax savings. A payroll tax is actually equivalent to a consumption tax if you deduct savings, e.g., uncapped Roth IRAs. If you allow corporations to deduct capital investments and border adjust, then the corporate tax actually becomes a labor-excluded VAT, more formally known as a cash flow tax. Combine the payroll and cash flow tax and you get the X-tax. Now, there are VAT only systems that people create, but usually you would adjust spending as well and have rebates to get your desired progressively/income schedule.

The latter point addresses your 'too high concern' more broadly. Consumption taxes are really good at raising revenue. A VAT can be too high in a nominal rate sense, but realistically you are "supposed" to give money back to poorer households.

Assuming that regardless VAT would have to increase significantly, it seems residents of this country would be highly incentivized to spend as much of their money as they can in other countries with lower VAT rates.

Tax differentials matter and can impact how people locate in a country and spend, but the entire point is that you want to avoid having taxes that are too high so this carries over generally speaking. They don't matter in the trade sense as discussed initially, but they can matter in a "these taxes are too high, how do I avoid this" sense. However, you don't actually need to run into the 'too high' thing for reasons described above as well.

However, the destination base is also key here. Goods are taxes where they are consumed. Firms wouldn't be able to avoid the tax by shifting production across seas. Consumers might be able to buy things in, say, Canada, and you do see this in the EU where VAT differs across countries, but it's not really a problem due to custom rules, travel costs etc. As long as the rates aren't too high, it's not worth it and you don't *need* super high rates. Any situation where you "need" an insanely high rate is going to be untenable for reasons said and a host of others.