When Stacey Richter’s husband recently landed in a New Jersey emergency room, fearing a heart attack, she had an additional reason for alarm: a potential big bill from the hospital if the E.R. wasn’t in his insurer’s network.

So she took an unusual step. Instead of simply signing the hospital’s financial and treatment consent form, Ms. Richter first crossed out sections calling for her to pay whatever amount the hospital charged. She wrote in her own payment rate of a “maximum of two times” what the federal government would pay under Medicare, which is in the ballpark, experts said, of what hospitals might consider an acceptable rate.

“And then I signed it, took a picture of it and handed it back to them,” said Ms. Richter, co-president of the consultancy Aventria Health Group.

Advocates say such consent-form alterations could provide some protection from surprise bills, though there are several major caveats to this largely untested idea.