I've been doing a lot of research on Constitutional conventions lately, and I wouldn't hold my breath on this working. It's too complex.
Just to review, there are two ways to get an amendment to the US Constitution, and only the legislative branches have the power to do it: A) 2/3 of Congress calls for a convention to propose an amendment or B) 2/3 of state legislatures pass resolutions calling for a convention to propose an amendment. The convention calls for delegates from all 50 states to come together and write an amendment. The delegates may only draft amendments that address the goals outlined in the resolutions. Once the amendment has been drafted, it's sent back to the states. When 75% of the states ratify (approve) the amendment, it becomes part of the Constitution.
Here's why Abbott's approach is shaky:
1) Each resolution calling for a Convention of the States must be identical from state to state. That means you'd need 34 states to call for an amendment convention with these 9 specific items. There are numerous states that have already passed resolutions for individual items on Abbott's list (balance the budget is a popular one), and they'd have to write and pass new resolutions for the Texas Plan.
2) The TX governor's plan is too conservative from the start. Republicans currently hold control of both the state House and state Senate in 32 states, but you'd still have to sway the Democrats in at least 2 other states. You might be able to sway Democrats on some of the issues, but certainly not all 9 at once. Again, breaking up the resolution would be the smarter approach.
3) Ratification. In order for an amendment to become part of the Constitution, 38 states need to approve it. The state legislatures vote on it. Right now there are 18 full blue Democrat and purple states. You might get a few of the new amendments ratified, but not all 9.
4) Shifting political landscape over time. I predict a liberal backlash in the state legislatures in two years. There's a nationwide push among progressives to repopulate the Democratic party with populists, and people across the country are organizing for the first time. While we might not see this in federal Congress, I definitely think we'll see a blue shift at the state level. This will make passing resolutions and ratifying amendments more difficult.