Fortunately, there is an answer to this problem: The House Judiciary Committee can launch an impeachment inquiry independently, without any vote by the full House.
And that's a good solution. Jerry Nadler, among others, is likely to be primaried next year, and this is a way to show the people in his New York district that he's willing to do what they want.
And if he does what's proposed, congressmen from more conservatives won't have to vote on an issue that may be controversial in their own districts.