You have left out a lot of needed information. I hope you don't mind my pointing it out.
1. Where do you live? it will make a big difference in how it can be transported.
2. How accurate is fairly accurate? Will make a huge difference in cost. From your description +-.050 would suffice but it would help if it were clearer.
3.What is a decent rate of speed? I think 1"/day is a decent rate of speed for this device. I am guessing that would not work for you. On a 12'x12' machine you would want at least 144"/min. this would give full axis travel in 1 minute.
4. Are you expecting that the $3K budget includes electronics and computer?
5.By dual axis I am assuming that you need an x-y table and a place to mount your Z axis/linear actuator.
6. How much clearance above the paper do you want or need?
7. A general sketch of what you are looking for would go a long way to getting it done.
Hope this is taken in the proper tone of helping you get what you want and not as picking on you. If I was not so busy at the moment I would be interested but I have had to turn away work to concentrate on my day job.