It is a lot of problem in your setup but it all depends on what you want to know and how big measurement errors that can be tolerated. Avoid metallic tripod, build something from the wooden pallets you have. Better if possible to measure with a VNA with time discriminator as all reflections are delayed compared to main signal.
Go outside! It is better and weather is not a problem. I do similar outside measurement even if it is raining or snowing with winds up to 30 m/s and -20 degree. Protect your equipment with clear plastic bags or something, avoid moisture in RF contacts. In case of thunderstorms, avoid measurements during flashes.
If you want to continue with an spectrum analyzer, build a transmitter connected to a simple dipole, via 1-2 meter coaxial cable ended with a resistor attenuator, as a reference unit. Dipole pattern is simple to verify and your system dynamic can also be verified by checking how deep your nulls are and that they are in correct place when you rotate the dipol. Use sleeves and a lot of ferrite tubes around all coaxial cables. Plenty. Check sleeve dipole at this link
**broken link removed**. It is a simple antenna to build, efficiency near 100% and its expected radiation pattern is well known.
Resistor attenuator must be built by SMD resistor in a screened box. Reason for attenuator is that you then know that your system impedance is under some control without being able to measure that and then avoids unwanted ground current.
Check fig4 at this link for a typical setup
Antenna Factors and Antenna Calibration.
If this is more then you is prepared to do, build at least a dipole and connect it to your DUT, it is done in 5 minutes. You only need some iron-wires and a coax cable. Also the copper-tube can be replaced by a few wires.
Whit this setup, check your max min radiation angels and signal levels in current environment. It is very likely that you then want to be outside and do your remaining measurements.