Not sure what you mean about "top of the curve", but I assume it means something like the pumps you are looking at are barely able to meet the flow demand, or on the edge.

80 gpm @ 300 feet of head is absolutely not a problem for centrifugal pumps.

Unless there is something you are not telling us, piston pumps would never be considered for that application.

Solution - You are not looking at the right pumps or right manufacturer.
That basic requirement of 80 gpm @ 300 feet is doable with 10,000 different pumps by 500 different manufacturers to start off, some will be eliminated by other criteria such as NPSHr, Ns, Nss, Efficiency, curve geometry, range, etc.

PUMPDESIGNER

What I mean by top of the curve is that a small change in pressure creates a big change in flow or I am essentially in the flat part of the curve.  I've been using the Bell & Gossett program to size the pump, but a difference in 5 psi may mean a change of 20 gpm.

I have spoken with Viking and they think a lobe pump would be the best application because of the thiness of ethlyene glycol at 135 degrees F.  I said that I might be able to change some of the arrangement and change the pressure drop to 200 feet of head.  They thought a gear pump might work.  I don't have much experience with lobe pumps. What do you think?

Gear pumps, designed for high temperatures, would not be a problem for this application.

http://www.haightpump.com/

There is no inherent problem in running on the flat part of a centrifugal pump curve; the pump will run at the intersection of the pump curve and the system curve whatever. If you are running pumps in parallel then you would have to beware. In this instance it is normal practice to fit a discharge restriction orifice to each pump before they common to prevent problems (you need a slightly higher head pump therefore).
If you are trying to run with no control on the system,then you will get fluctuation, but if you want no fluctuation you will have some sort of control system.

I cannot see anything in what you are saying that prevents the use of a centrifugal pump.

B&G has a centrifugal pump that will work in this application.  Contact your local rep and they can help with the sizing.  If you have just a single circut, check out the B&G triple duty valve, it is a shut off, check and flow control valve all in one.  You can set the valve to your desired flow rate.  As tonyh mentioned, this will require a slightly higher head pump, but B&G has all the information you need to calculate the additional pressure loss.

Although meant to render a constant flow rate at constant speed of rotation, gear pumps may be mechanically sensitive to temperature variations and shocks in regard to the thermal expansion of its parts, and the resulting changes in clearances, and possible pump or seal damage.
0^oF is a cryogenic condition that may require pre-cooling of the pump. Anyway, materials of construction should be selected accordingly.

As for myself, I don't see why a centrifugal couldn't meet the requested operating conditions with suitable flow control devices.

EG is considered somewhat toxic and should be handled with care.