O.k. Success. But it wasn't a reflow.
Turns out the first SIMM socket must be a little slack, and maybe just maybe, the pins don't always make solid contact. So I've improvised and used a small plastic wedge to hold the SIMM enough to reach the pins.
I may replace the SIMM socket eventually, but for now we're done and back in business.
Falcon CT60, Falcon CT63 x2, TT x3, MegaST x2, MegaSTE x2, STFM x2, STE x2, STacy, STBook, (Dead) Hades 060, Milan 060, T40.