Multiple Accounts under 1 project

We often provide quotes to multiple contractors under 1 project name. Sometimes it takes many months before the low bidder can be determined, so we want to be able to track all the contractors we know of throughout the bid process.
Currently, the default setup is to clone a project many times, which looks a bit odd when viewing open jobs.
Another setup we tried is to create a general Account Name with a specific stage of TBD, however, this still doesn't work because it only gets assigned to one user - yes we could run a report to pull the specific stage, but this isn't a great way to use our time.
The 3rd option was to create new lookupfields in the project name. However, the new lookup fields don't show up under the job setting in the account view, so our users would have to scroll to the bottom and look in a second location for open jobs. This too isn't an efficient solution. Also, these new lookup fields cannot get pulled into job reporting in the same format as general job reporting.

So, how do you propose creating multiple accounts under 1 project so that the project name shows up in the job field, and gets reported appropriately?

Thanks,