Which tube does the Little Dot need? I may be able to give you some advice with my experience with the tube.
I think you can buy the AE-3 for under $500, maybe not the latest or fanciest models. Many AE-3s had remote control, so that isn't always a problem. Tube rolling is most important with it's amplification tubes which are 6SN7s. Fortunately these are abundant as NOS/OS and there are many bargains to be had outside the most sought after versions. Some models are tube rectified but they too are not overly expensive or rare, and plenty of people are satisfied with current production.
I think you can buy the AE-3 for under $500, maybe not the latest or fanciest models. Many AE-3s had remote control, so that isn't always a problem. Tube rolling is most important with it's amplification tubes which are 6SN7s. Fortunately these are abundant as NOS/OS and there are many bargains to be had outside the most sought after versions. Some models are tube rectified but they too are not overly expensive or rare, and plenty of people are satisfied with current production.