Need suggestions for evicting 1 of 4 roommates

[AJ Pryor]

I recently purchased a 4BR rental property in a college town in the state of Georgia and took over an existing lease that ends in July of this year. The lease is a separate agreement for each tenant such that each has their own agreement for 1/4 of the total rent. This is a headache, and once the lease expires I'll put a new one with all four names responsible for a single amount of rent, but for now I am stuck with individuals.

One of the tenants has not paid rent for the month. I've served a Pay or Quit and will now move forward with the formal eviction process. I have a double problem, as upon reviewing the lease documents turned over at closing I discovered that there are only 3 signatures, and naturally the tenant who has not paid is the one missing. There was apparently a previous roommate, some drama, and this was the replacement tenant. This person did pay rent for one month (though late, piece-by-piece)

I'm not sure what the best path is forward for the remainder of the lease and am looking for suggestions. What I've thought so far is I could:

1) Advertise and fill the BR on my own with either a month-to-month lease or a shortened term that coincides with the end of the existing leases

2) Offer the other 3 tenants the opportunity to find a new roommate, but if they choose to do so require that they cover the missing rent until they find another roommate. This presumably could be done by a secondary agreement. The idea here is that people like to, well, like their roommates and they probably prefer to pick, but I'm concerned if I just leave an open time window I'll end up in the same position, just further down the road and out of pocket.

3) Indicate to the remaining tenants that they must cover the missing rent. Given the terms of the agreement, I don't think this is an option.

And, again, the fact that the lease is missing this person's signature makes me fear I have no legal foothold here. A painful lesson to learn going forward -- but can somebody provide insight into what my options may be?