Prior to initiating GBAS service in equatorial regions, it is vital to evaluate potential integrity threats posed by equatorial plasma bubble (EPB)-induced ionospheric gradients and assess availability when implementing ionospheric threat mitigation methods. Earlier work developed a preliminary EPB model with a gradient bound larger than twice that for mid-latitude ionospheric storms. Position-domain geometry screening (PDGS) with this higher gradient bound decreases availability to 58.3% at the Galeao International Airport, Brazil, during nighttime. A new mitigation method using Monte Carlo simulation randomizes ionospheric scenarios using randomly generated parameter combinations within the threat model and assesses the ensemble impacts. By taking credit for a prior probability of an extreme EPB, this algorithm determines the inflated integrity parameters to meet the safety requirement in the probabilistic definition. This paper shows that with this method, the system availability for category I precision approaches dramatically improved to 89.6% when a data-driven prior probability of 10-5 was applied.