A partition action is equitable in nature (e.g., equitable not legal remedies available, no jury trial, etc.) Thus, assuming you want to keep the property based on your stated effort to buy out your ex-girlfriend, courts routinely allow an accounting so that the respective rights of the parties may be adjusted and settled. An accounting would entitle you to a credit of your share of contributions that are not matched by your ex. To avoid the impasse over an appropriate purchase price, consider asking the court to issue an order (1) appointing one or more appraiser and (2) fixing the purchase price as the average of all (or just the court-appointed) appraisals.
First the credits for both parties and how title is held and finally do they agree on value. If they do not agree and the difference is great deal, the judge will probably order it sold and let the market determine the fair value.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none.