You could try a digital caliper to get the measurement perfect.
If not that you could push a pin through the inside going out and see if it moves when the driver is under full excursion. Of course make sure the pin has got tape or something so it doesn’t damage the surround.
I’m interested though in a best practice rather than trying all that.
You can also use that green foam used for flower arrangements, just stick it in bag before you use it so it doesn't make too much mess. I have some plasticine-like modelling clay and some polymer clay, and both blocks are a bit on the firm side for measuring speaker clearance since they're firm enough to slightly bend an ABS door panel. Softer stuff does certainly exist.
The problem with sticking a paperclip or other feeler rod through the grill is that you might accidentally have the feeler tilted at an angle and that will throw your measurement off. For measuring speaker grill clearance, you probably want the measurement to be perpendicular to the mounting flange.
Play-doh or a homemade version of it would work instead of actual modelling clay-- it's not like you're going to keep this thing like its a special sculpture, so the clay or foam itself doesn't need to last.