If you really do prefer a quant study vs. qual then quant like Frederic mentioned, it may make sense for you to just do some legwork to try and gather a list of email addresses and phone numbers of potential target respondents. Reach out to them and offer a small honeraria for completing your survey.
To be honest, if you have a hard to reach respondent pool, that's what most MR firms do anyways, just on a larger scale.