Probably because our goal is to find out what Earth's temperature as a function of CO2 in the atmosphere is, we have no equation for it, we don't know the terms, many of which are also functions of CO2, many of those terms have joined terms which can increase or decrease as the other term does the same - positive feedback or can do the exact opposite - negative feedback.

Take a cloud, a large white mass mid air reflects away light coming in form the sun, and absorbs infrared, it also reflects reflected light back from the surface to the ground again, giving the energy another chance to shift to infrared, but its presence blocking the sun means little light gets through to be reflected to begin with. Warmer temps, more water vapor in the air, more clouds, higher insulator effect and higher mirror effect. That higher reflectivity is a negative feedback, that higher IR absorption would be a positive feedback, but their relative value will not remain the same to each other with temperature, even if one term is consistently larger the amount by which it is large would not remain constant. Further those terms will shift again with temperature because cloud quantity will change with temp, and clouds of different types have a different ratio of reflect/absorb and temp changes the mix of those as do other factors that themselves are Dependant on temp, and most are dependent on other variables as well, which may themselves be effected by temp or CO2.

Let me point out a few breakdowns that will happen in your experiment:

1. Cover the roof in doors with several lamps that not only provide light, but UV rays as well. If they don't have bulbs that produce both, the you can alternate light and UV bulbs. The idea here is to simulate the sun.

No. You would first have to evacuate all air from around the house, or the experiment is pointless, as they significantly alter the thermodynamics of heat exchange on the surface and would also allow convective effects to take non-light energy from the bulbs to the house, as is, only by using LED lights could you significantly reduce the amount of secondary frequencies of light from heating the house, and we can not yet simulate solar spectra that exactly. Remember that while the sun does have some strong bands of emission most of its light is from blackbody radiation, replicating individual frequencies is not too hard, but those all have other wavelengths - secondary peaks and such. Adding up all sorts of various lights can ensure that the right quantities of light are emitted to roughly the right amounts, but you'd almost surely have other frequencies appearing in greater quantity then desired.

Further, the nature of the beast would require that the house be evacuated on all sides, or you have conductive heat transfer of a massive degree, so up on stilts made of very non-heat-conductive materials and in a vacuum

And the house has the wrong geometry, heat exchange even in a vacuum is still a matter of geometry as much as it is materials and net energy input/output

2. Have numerous temperature probes along the floor and around the room, constantly monitoring temperatures. Also, add CO2 detectors at various heights around the room..it would be a good idea to put the CO2 and temp probes together.

Very good. If your lights are inside the house, all light emitted will be captured and released as IR frequencies, unlike the Earth, as CO2 absorbs IR very well, your temperature will increase. As we say, the only 100% efficient device you can make is a heater, if you have electric heater sin your house for instance, instead of gas or wood, so long as you close your curtains you can leave the lights and TV and fridge on non-stop, you electric bill will be the same, all the energy they use will end up as light. A 500 W TV and a 500 W heater and 5 100-w light bulbs will all warm your house just as well for the same cost, almost, you'll probably leak some light energy through windows and kinetic energy through sound from the TV, not much though.

3. Turn on lamps and allow ambient temperature to achieve stability for a few hours. Turn off lamps and monitor the time it takes for the temperature to cool and stabilize. Do this multiple times to gather enough data for control.

Good

4. Repeat step 3, but fill the room with CO2 to varying degrees. Something like 10 ppm the first set of trials, 20 ppm the 2nd, etc. Monitor the time it takes to cool and stabilize.

No Change, if the house were made of glass this would work, however, while CO2 is a good IR absorber, lots of other stuff is, in your opaque environ everything that is not 100% transparent to IR frequencies will gather that heat just as well, and via convective and conductive transfer will spread the heat to everything that is less good at absorbing IR, the know dominant effect in cooling will be the exterior material and it's geometry and thermal properties, and heat will be drawn form the CO2 bearing air no differently then normal, it will rapidly normalize to your walls and stay that way

When skeptics say we can't exactly match the conditions on Earth for these simulations, they aren't talking about being off by some trifling sum. The reason ice core samples are considered a good measurement is because we can extrapolate long plots of CO2 and temperature for comparison.

What you're trying to get at with your experiment, that CO2 absorbs IR, is not something 'Skeptics' need demonstrated in the first place, they are not stupid and know this. It can be demonstrated with far simpler means, has been demonstrated beyond question, and is not to my knowledge under dispute by any 'skeptics'. One need only get a laser and sensors of a desired frequency, and place them around a box, with the laser aimed at one of the sensors, as you fill it with more CO2 you can see how transmission drops off and the other sensors will let you calculate reflection, scatter, etc. Needless to say this has been done to virtually every common material and done under many different extra parameters, from running electrical current through it, or under different pressure, temps, etc - hence the invention of Liquid Crystals, which change their absorption and transmission properties based on temperature, electric current, pressure, etc. Presumably you are staring at a bunch of such examples right now, individual pixels whose interior is full of material that if exposed to a a current will become transparent or opaque, thus letting light pass through, needless to say CO2 is far simpler, and its thermal and light functions have been tested under thousands of different scenarios, as have most terrestrially common gases, since they were the easiest to work with, their properties in these respects are not under serious dispute, your suggested experiment only shows you do not understand the nature of the objections to AGW.