I think I found the culprit.
I started commenting away directives, starting from the end, to find at which point the bogus "Equity:Conversions" (a few dollars) starts showing up.
This occurs immediately after including an entry that looks something like this:
Assets:EUR 0.000000004 EUR { 0.84379 USD }
Expenses:CapitalLoss:EUR 0.000000000004180176 USD
What this is doing is closing down (partially or fully) a EUR lot (which we know exists because Beancount allows me to do it without showing any errors) and booking a loss for this lot. As you can see, very small near-zero amounts.
Could the sudden introduction of the bogus conversion entry (a few dollars) be because of some floating-point calculation issues related to these near-zero amounts? If so, can I increase the precision of this calculation, so I can test if that gets rid of the bogus conversion entry?