I don't have any ideas beyond what was already stated. However, to be "that guy", I humbly suggest that you may not be able to afford a 5-6K car if you do not have $2500 on hand. Your goal is to get to a point where $2500 is a notable, yet ultimately inconsequential outflow and it will be challenging to get to that point if you keep borrowing.
Also, please consider the added expenses of vehicle maintenance, insurance, registration, etc to counterweight your monthly savings from Lyft, etc. However, $250 a month is not bad if that is your only commute expenses and meets your needs. Could you also get a bike? If you truly need a car, I would suggest a ugly beater for a portion of the cash you have on hand. Your first urge may be to feel embarrassed, but take pride in the lack of debt and sacrifice you're willing to make.