I'm not sure what you mean by "one with stops for long shutter exposure" for astrophotography. For astrophotography the head has to keep moving -- specifically at something called "sidereal" speed. That means it does a completely rotation in 23 hours 56 minutes and 4 seconds. That's the true speed at which the Earth rotates on it's axis (not 24 hours). The Earth advances about 1º in it's orbit around the sun per day. So while the Earth has rotated 360º in slightly less than a day, the Sun will appear to have moved (due to the Earth's orbit around the Sun) and that's where it takes nearly 4 more minutes of Earth rotating before the Sun returns to the same point in the sky (e.g. local noon one day until local noon the following day.)
There are numerous video panning heads but I'm not aware of any that can rotate continuously (most control tilt as well as pan and that means they have to run wires to the tilt-axis and that creates an internal wire-wraps problem -- so products like the Bescor MP-360 give you a 360º rotation... just not continuously (CamRanger sells the MP-360 head so that it can be remotely controlled via a smart-device such as an Apple or Google phone or tablet. And then of course you have to own the CamRanger itself and still buy the MP-360 so the price adds up.) These tracking heads do not have speeds appropriate for astrophotography.
Though I do most of my astro-imaging with a telescope and a Losmandy G11 mount, I *just* acquired a Losmandy StarLapse system -- which is intended to mount on photo tripods and hold cameras rather than telescopes.
See:
Losmandy StarLapse System
I haven't done any "real" work with it yet other than just some quick tests to make sure it's working. I'm planning to use it extensively on an upcoming trip to Hawaii which has CONSIDERABLY better dark-skies and steadier atmosphere conditions than I can normally get. Bringing my imaging telescope and mount would be impractical (and I'd be terrified that the airline baggage handlers would damage it.) So the StarLapse system (which would fit in a carry-on case) is ideal.
There are a number of tracking and panning heads. For astrophotography there's the Vixen Polarie, the iOptron SkyTracker, and the AstroTrac (in addition to the Losmandy StarLapse that I mentioned already). But the Vixen and iOptron products have very limited tacking rates and can't track at a rotation speed of 360º in 3-4 hours like you mentioned above and the AstroTrac is basically a modern "barn door" tracker so it can't even do a 360º rotation. I think this means you'd have to scratch all of these other heads off your list.
It actually can rotate continuously (it's not limited to 360º) and it has 9 selectable tracking rates, which include:
1) Sidereal speed (23 hrs 56 mins 4 seconds to complete a 360º circle. This is actually the speed that the Earth turns and that's why it has to be the speed to track the stars for long exposure astrophotography)
2) Solar speed (24 hours to complete a 360º circle.)
3-9) 7.5, 20, 30, 40, 60, 120, and 240 degrees per hour. For example, picking the 120º/hr rate would mean that it would complete a 360º rotation in 3 hours. (BTW, it does not stop until you turn it off and once you set the tracking rate and start it, it locks out changes until you turn it off. This prevents someone from bumping a control, changing it's tracking speed, and thus destroying hours worth of careful work because you don't find out that the tracking rate got changed until you review your images later.)
Based on this, it *might* be the only product that does everything you want.
Another nice thing about the Losmandy is that it's designed to keep the camera neutrally balanced while in operation. If a camera isn't balanced then it would put either more load or less load on the motor as it rotates (depending on whether it's lifting the weight of a lens or if the lens is on it's way back down to the opposite horizon.) On the Losmandy system, the camera mount slides along a bar (actually there are a few adjustments) so that the thing is mounted so that it's center of gravity is position at the rotation axis. That means the load on the motor won't change over the hours and the tracking rate will remain consistent (it's a very well thought-out and engineered piece of gear.)
To do astro-imaging you still need a tripod head that can let you adjust the tilt angle (a video head works better than a photo / ball-head) so that the rotation axis of the StarLapse points to the north celestial pole (the pole-star ... Polaris in the northern hemisphere ... is about 2/3º away from the pole but usually close enough for wide-field images. For longer focal length lenses they do sell an optional polar-alignment scope that installs in the center of the unit and it has an illuminated etched reticle alignment aids that helps you do much more precise polar alignment.)