Question
I know our quality of service is far superior, and I know that all the people (or at least 90% of the people) pitching lower prices than us won't be able to deliver an end product that will be of much benefit to the client (even if they do manage to fulfil the technical requirements).
We want to actually talk to buyers to figure out how and if we can actually help them, but most insist on us just sending a quote so they can screen everyone based on pricing before proceeding to discussions.
Answer
Might I suggest a referral program? If your service and quality are above your competition there, referrals should eventually take over as your main source of business.
Think of ways to encourage that behavior without being annoying. Offer some cool kickbacks. Give out some apple watches.
IMO, those sites are nothing but a rat race to the lowest dollar. Know your value and demand it before you take on a project.