The very first thing I would do is get a copy of what you signed immediately, even if it means getting a lawyer to request it - you don't want them to come back to you at some point in future (whether or not you're still there) and try to collect for a year. Give the recording (a copy, rather) to the lawyer and see what he has to say, but I'm not sure what it is you want yourself at this point, as you said you're going to be moving in any case (did you tell that to the management - if so, it might explain their actions).

I was able to find your State by the videos you posted, and then googled the apartment complex.

I'm not taking sides, just pointing out a few things I see that might help or hurt in your situation. ;)

First, bad idea to deduct anything from the rent you owe. A lease is a contract with a set rate of payment for a set period of time. Paying less is a breach of that contract in some states. I understand what you were trying to do, but there are other avenues to try to resolve your problem that don't put you in jeopardy of violating your lease agreement or being evicted for failure to pay. (Unless, of course, mgmt agreed to it, then it's non-issue.) Your State has very specific guidelines on that matter. The Tenant's Rights link below addresses this very topic, not bug infestation specifically, but it gives an outline of how the procedure is to work. Much more specific than my State.

Secondly, very bad idea to post a video on You Tube and name the complex. In fact you've got 5 up that I see. I'm not sure what positive results you thought that might bring? There are proper venues to pursue (see links below). This isn't one of them. You have to know that surely someone has seen that and have immediately crossed that complex off their list of possible places to live. Yet you've expressed you want to continue to live there, negotiated a new lease agreement, and then publicize how atrocious the living conditions are. Trying to pressure them using that kind of negative publicity will boomerang on you. It's not going to do anything productive to help your case and it's absolutely defamatory toward them. I'm not saying they are not responsible for addressing the problem. What I am saying is the problem could occur in a number of ways and you cant' be certain how. You're placing 100% of the blame on the complex, but what if the guy next door to you is living in a manner that perpetually invites pests? What if mgmt treats the problem (perhaps while you're at work) but the slob next door brings back more bugs? My point is you can't say with 100% certainty that they've not treated (since it could have been done outside of your presence). Since the complex name was listed I googled it. Complex information comes up first, but your videos also come up on the first page of google hits. It's just a matter of when, not if, they see those videos and there's just nothing productive that can come of it for you. In fact it could hurt you more than help you. I'd urge you to remove them right away to avoid setting yourself up for some nastier problems, possibly legal action.

I signed the lease but they would not give me a copy of the renewal papers. If you signed and mgmt signed, but refuse to give you a copy, you're going to need to get in touch with either an attorney or someone who handles landlord tenant affairs for your State. If you signed but mgmt has not signed, yet money has been exchanged, the law in your state would probably view that as a verbal contract since money exchanged hands. Here are some links for you to look at that cover this:
Tenant's rights. It's very well written and very explicit.
Part two of that link.
Attornye General Tenant's Rights

Tenant Advisor (contact information at the bottom)

When I insisted they say they will tear off the lease papers and charge me month to month. They can't tear up an existing contract. It's a legally binding agreement and if they want to get out of it before it expires they have to use legal avenues.

Have you told them of your intent to purchase a home in the fall? I'm wondering if they are not bringing up a monthly lease because they know if they renew for a year that you plan on breaking the lease early? If that's the case, and you know for certain you are leaving before a full year is up, you're better off with a month to month lease. Of course, that makes it easier for them to get you out. All the more reason to take those videos off the internet.

I recorded that conversation. In many states making an audio recording of a conversation with someone without their knowledge and consent is a felony. Check your state law here on that. (Click state-by-state guide in the left menu.) If it's not legal you can't use it and I sure wouldn't tell them you're taping them.

Just a final thought: you're spending a lot of energy it would seem in a 'battle', posting videos and taping conversations. But your energy is misdirected. Focus and channel it in ways that are productive to you, not harmful. Read those links and utilize the contacts and resources. Otherwise you're setting yourself up for backlash.