There is latitude in headset stack height, but it's limited.

You can always go with a shorter headset and use spacers if you need to make up the difference. However, higher stack heights are a problem unless you have a source for negative space spacers (which are very pricey). You may have 1-2mm upside room, maybe a bit more, and the eay to know is to remove the top nut while leaving the rest alone. IMO you want at least 3mm (barest minimum) of thread engagement, so if, for example, there's 5mm now, you have a bit of cheat room. Likewise if the replacement headset stack height includes a spacer you can live without.

Unlike your assumption, headsets are much easier to substitute than BBs, so you should be able to approach his with a bit of confidence.