1st Amendment exceptions do sometimes hinge on whether or not less burdensome alternatives were explored first. IANAL, but "you didn't even think if there were other ways to accomplish the same goals" can be a factor in deciding whether speech restrictions are over-burdensome.
If I remember correctly, this came up a couple of times during Covid over religious gathering restrictions -- the question was less "can the government ever restrict a religious gathering" and more "is it actually necessary for you to do this? Have you taken steps to minimize the burden, is the burden imposed greater than the state's specific need for this restriction?"
How a judge would rule on that in this case... :shrug:, but it doesn't seem to be an uncommon argument. There have been Supreme Court ruling that boil down to, "it's not unconstitutional necessarily but you did it wrong and we think you were too slapdash doing it, so try again."