Ex-employer refusing to pay me ~$11,500 in back pay (Texas)

I'll try and keep this as brief as possible. I apologize for the wall of text below. Looking for advice on next steps to recoup the ~$11,500 I am owed in back wages that my ex-employer is refusing to pay me.

I live and work in Texas. Until just recently, I worked as a medical director for a hospice agency as a side hustle so to speak. During my < 1 year working there, I realized just how shady and immoral the administrators were who hired and employed me. I eventually gave them my (contractually obligated) 60 days notice on July 1st, with my employment technically finishing at the end of August (though no further work was assigned to me after I gave them notice).

My work in June should have netted me ~$4,500. When mid July came and went without pay, they said I'd get it at the end of July (which was technically still Kosher as my contract read "Payment will be made by Hospice within 30 days after the end of each month during the term of this agreement"). But when that came and went, they claimed "we're in a financial situation" and said they'd get me whatever they could (not the full amount) by mid August.

In addition, they tried to pull a shady move and avoid paying me for 2 months of work ($3,500 x 2 = $7,000) at the end of last year. At the time I made a big stink saying if this wasn't rectified I'd quit immediately. They responded by adding a signed addendum to my contract that reads: "Two payments of 3500 equal to $7000.00 at the end of the contract timeline the agency reserves the right to pay this amount prior to the end of the contract, providing the medical director is made aware of payment prior to payment made."

So in sum, they owed me $4,500 by the end of July, and $11,500 by the end of August. When they told me they were in a "financial" situation in early August, I responded that I planned to file a "Wage Claim" with the "Texas Workforce Commission" if they did not actually pay up. At this point, they stopped responding to my messages. Then I saw one of these administrators in my regular hospital, and upon confronting him, he said "We got your message. Do what you have to do." Essentially saying tough shit, we aren't paying you, you'll have to take it from us.

In reviewing my contract, there is a clause that states matters would need to be dealt with via arbitration. Specifically:

"Arbitration. Any dispute relating to this Agreement will be settled by binding arbitration conducted in accordance with the Health Care Arbitration Rules of the NHLA Alternative Dispute Resolution Service (c/o National Health Lawyers Association, 1620 Eye Street, NW, Washington, DC 20006). THE PARTIES UNDERSTAND AND ACKNOWLEDGE THAT, BY AGREEING TO BINDING ARBITRATION, THE PARTIES WAIVE THE RIGHT TO SUBMIT THE DISPUTE FOR DETERMINATION BY A COURT AND THEREBY ALSO WAIVE THE RIGHT TO A JURY TRIAL. THE PARTIES UNDERSTAND AND ACKNOWLEDGE THAT THE GROUNDS FOR APPEAL OF AN ARBITRATION AWARD ARE VERY LIMITED COMPARED TO A COURT JUDGMENT OR JURY VERDICT. THE PARTIES FURTHER UNDERSTAND AND ACKNOWLEDGE THAT THEY HAVE BEEN ADVISED OF THEIR RIGHTS TO CONSULT WITH AN ATTORNEY REGARDING THIS ARBITRATION AGREEMENT PRIOR TO EXECUTING THIS ARBITRATION AGREEMENT, AND BY EACH PARTY'S SIGNATURE BELOW, EACH PARTY ACKNOWLEDGES THAT IT HAS EITHER CONSULTED WITH AN ATTORNEY, OR HAS HAD THE OPPORTUNITY TO CONSULT WITH AN ATTORNEY WITH REGARD TO THIS ARBITRATION AGREEMENT BUT HAS ELECTED NOT TO DO SO."

So my understanding is, because of this clause, I can't outright sue them in court, and would need to take them to arbitration.

So, my first step is to file a wage claim with the Texas workforce commission (which I intend to do today). But, being the cynic that I am, I can't imagine this will do much of anything. I'm wondering what my next steps should be.

I can be a petty and vindictive asshole, and so far I've already lobbied the administration at my hospital to cut ties with this agency and to stop referring patients to them. In addition, I plan to review bomb them online. But that's just for me, and it won't do anything to recoup my money.

After the Texas Workforce Commission, what steps do I take? How do I even bring a company like this to arbitration? Are there any other steps I can take to get my money back? To be honest, I'm already assuming I'll never see this money, but I'm also stubborn and refuse to give up so easily.

Looking for advice from an anonymous Reddit lawyer! Thanks!