Get you a crossbow and kill them in archery season. The area of the county I live in has no doe harvest season at anytime, unless you are a member of the county WMA. In my area if you are not a member of the WMA then you can not kill any does. If you are then you can get doe permits based off of the county wide surveys done and your acreage.
Also a lot depends on your TPWD biologist. Some are more acceptable than others to MLD. IMO I do not see you getting an MLD with small acreage. Pooling acreage together with neighbors is an option but can become an issue over time with how tags are allotted.
One other permit is the ADCP or Antlerless Deer Control Permit for dealing with over population problems for does/spikes. IIRC you have to pay for this permit. https://tpwd.texas.gov/publications/pwdf...ermits_info.pdf