I spent several years working on projects to automate construction / mining equipment that required highly accurate location values. At the start, we could use GPS fairly effectively for vehicles moving down a pre-defined path, but had to switch to GPS + RTK base stations when looking to get < 1M accuracy needed for things like loading dump trucks, etc.
Originally, RTK units were very expensive (as in $80K for a base station and another $20-40K on each vehicle) which limited the range of applications. But the price has dropped tremendously. The last set of items I built for this used a variety of GPS+RTK boards that brought the whole system below $300. Sparkfun makes one such board.
With these systems, you can get down to the sub-centimeter range. So ... really accurate. But you're still going to spend $200-400 if you want to track movement that accurately.
To get the kind of .5M accuracy you're looking for, look for a GPS chip that incorporates GLONASS and Galileo (which is, honestly, just about every new chip). Your device is moving slowly, so you could do something like sample four times a second and take a rolling average. You'll probably have to do some smoothing and filtering, because momentary blockages of satellites can result in an abrupt apparent shift in position and sometimes GPS just gives a "WTH" value. But it can definitely be done.
Oh, and there's really no limit on how often you can check GPS signals. Several libraries out there do try to slow things down, or just feed you the same results if you ask again repeatedly, because GPS can be a power hog. But if you have the power, just take more measurements.