You could exercise your rights, but then I'm afraid they would just give you 30 days notice to move out on March 1st. You could then take them to court, but you could end up having to move, then fighting them in court, and pay a lawyer a bunch of money.
From your OP, it looks to me like 1) you don't want to spend any more extra money than you have to; and 2) you don't want to move until at least end of June.
So, basically, the PM wants you to either sign a 7 or 12 month contract - and you can pay the same amount of rent.
Or, you can continue month-to-month and pay at least $400 more a month, and they may change that every month.
You want to stay through June at least. 4 months.
In TX, a LL must mitigate damages. This means, that if you break the lease, the LL has to make a reasonable effort to re-rent the unit asap. BUT, TX law doesn't specify how the LL has to do this, and even allows the LL to raise the rent and try to rent it at a new price. So, this "right" is a bit iffy in TX.
So, let's do a little math:
1) You can offer to sign a 4 month lease at the same rate of rent.
This costs you nothing extra.
They'll probably say no. Then you could try sweetening the deal by offering to pay, say, $200 more per month for a 4 month lease through June.
This would cost you $800 in additional rent.
If they agree.
2) You can agree to sign a 7 month lease at the same rent you are paying now. How much is your current rent?
Let's say if you do this, you find a place to buy after 5 months into the lease. Then you break the lease. In this scenario, you can expect to lose up to 2 months rent - the remaining time on the lease. You'll want to also read the lease carefully, to see if they can also keep your security deposit for breaking the lease. I'm not sure on the law regarding this.
This would cost you 1 - 2 months rent. And maybe your security deposit.
BUT! If you don't find a house to buy during the entire 7 months, you're not out any extra money.
3) You agree to go month-to-month and pay the additional $400/month. Of course here, they may keep upping the rent beyond the $400. Let's say you find a place in 5 months (same as above).
This would cost you $400 x 5 = $2,000 at least.
If I were you, I'd start by asking them if you can sign a 4 month lease at the same rent amount -
if you really think you could close on a new house and be ready to move by July 1st. Be aware that they may not let you go month to month again after this agreement.
If you're not sure about closing and being ready to move by July 1st, I think I'd go ahead and sign a 7 month lease.
None are perfect options, but I'm thinking it's your best gamble.
Here are some TX law resources:
http://recenter.tamu.edu/pdf/1513.pdf
Breaking a Lease and Leaving Early | Nolo.com
A Landlord's Duty to Mitigate Leases in Texas | eHow
Texas Tenant Advisor