Increasing MR Survey Response Rates

My organization is relatively new at launching market research surveys, so I'm still learning some of the ins-and-outs of increasing participation. I could use the opinions of some seasoned MR folks for my distribution problem...

I want the sponsor of my survey to remain anonymous (revealing my company name may skew results). We have contracted with a panel provider, who couldn't get _quite_ the numbers I needed for a statistically representative sample. So I want to supplement the panelist numbers with a few responses with contact info sourced from a B2B 3rd party contact provider.

The panel provider company misunderstood where this list came from; while initially they agreed to do the distribution to my email list on my behalf (keep my company's name out of it), now they are saying they can't work with contacts sourced from a 3rd party. So now I'm stuck with not only a problem, but a limited time frame to fix it.

We do have an appropriate incentive attached. Any ideas on how to execute this? Do I just send the email through qualtrics without a signature/sponsor and hope people don't regard it as spam? Any other ways to get this distribution out that I'm not thinking of?