Setting up CRM for RFP workflow management

This will be the first time our organization uses an off-the-shelf CRM, transitioning from our homegrown custom solution, and I would appreciate general thoughts on how to get started in general with our workflow using Zoho CRM. The main question: if we focus only on RFPs for our business, do we use opportunities and/or Deals (and ignore Contacts and Accounts entirely?) Our business process is as follows:

We apply for RFPs and RFIs that are listed in various government listings, mostly local government agencies, so our potential field of clients is in the thousands. (just wish our customer count was also in the thousands! :)
Our industry does not do sales calls or have leads. No names are generally attached to these opportunities, except for the contract officer, but he/she are not critical to be tracked in our process. And they are surely not a primary or required field when we enter an opportunity.
In our current customized system, we enter an opportunity by the project name and the title in the RFI or RFP. Again, no person names are provided or given.
Once we apply, we wait until a review panel scores all the applicants' submissions and we get to a finalist round or perhaps move straight to award.
After award (if we are successful), in our customized system, this automatically moves the opportunity to our project management tab where we track progress, mods, milestones, etc.
Our company is organized into four teams, but no one has "accounts." We may see and pursue opportunities from the same client from time to time, but the client is never considered an "account," either.

Of course, nothing about this is entirely unique. But from how I am trying to set up the CRM, it seems I should ignore/hire the Accounts and Contacts tabs and only focus on the "Deals" or the "Opportunities" tab? Both seem to focus on an individual though, so the workflow seems like square peg/round hole.

Thanks for helping nudge me in the right direction.