The lease is confusing because it states the guarantor is a condition precedent, which should affect your obligatiosn as well as theirs, but then in the same paragraph it states that they have the right to withhold possession and continue to charge rent.
I believe that would be held as unenforceable, since they have the right to approve or not approve a guarantor and then continue to charge rent without having to provide possession.
If you are in a position to litigate this I think you stand a better than fair chance of prevailing. The provision is predatory, abusive and inequitable. Additionally, the provision is vague and vagueness is interpreted agaisnt the drafting party.
Remember, though, it is risky to sign another lease. There is always the possibility that the landlord will seek to enforce the lease and you could be stuck with two leases.
Therefore, you may want to see if you can negotiate a settlement with the landlord. Perhaps an extra month of security deposit would induce them to drop the guarantor. Otherwise, they would have to sue you to collect the rent and I think a court would have a hard time enforcing this onerous a provision against a tenant. I believe they would tell the landlord that if the condition precedent has failed then they can terminate the lease or waive the guarantor requirement.