I second the recommendation for full-year acceleration, if applicable. Your story sounds very familiar to me, and after many attempts to do it the school's way, we finally crammed a full-year acceleration down their throats, and it was the only solution that managed to work for a full school year. Most of their solutions were successful for periods best measured in days, if that.
We heard the "gaps" argument many times, and asked them to administer an assessment to identify whether that concern was valid, and if so, help us to address them in order to make a grade skip successful. They refused. You've already got that data, and it confirms that gaps are not an issue. Not many end-of-third graders can pass an end-of-third grade math test with 89%, nevermind a three-quarters-through-first grader. And in any case, you're asking for a single year skip, so you'd be putting her in beginning of third grade next year - assuming the gifted class is one year ahead (many say that but don't deliver), that would put her at beginning of 4th, a very appropriate placement.
Re: #3 - Aquinas has indicated that it's working for her DS, but your mileage may vary. My DD experienced something similar in K. DD found herself completely isolated socially (and she's an extrovert), received zero teacher support (and she's not an autodidact), and the whole thing went very poorly. DD vacillated between hating herself for not having friends, and hating herself because she was too stupid for the math program, and must be an intellectual fraud.
Depends on the personality of the child.
