We're using a 1.5" peristaltic pump to empty a vertical container in a smooth and stable rate (around 30L/min).
What we noticed is a repeatable distortion in the flow rate caused by the peristaltic tube volume change due to the pump
Roller engagement, causing momentary back flow. This phenomena is highly unwanted by us since it causes a pulsing  flow pattern.
We're looking for a solution for that.

A peristaltic pump is a rotating positive displacement pump but creates pulsations like an oscillating PD pump. Oscillating PD pumps usually come along with an appropiately sizes pulsation dampener but I have never seens this as standard for a peristaltic pump. A pulsation dampener (air over liquid or bladder type) will solve that problem if correctly sized. 

A progressive cavity pump is as sensitive to solids as a gear pump is.

Your problems are backflow and pulsations, right? And you want a constant flow which is independend upon the suction head. A triplex plunger pump is too big and too expensive for your low flow and pressure. Furthermore plunger seals do not like solids neither. A triplex diaphragm pump is expensive, too. But a small double head diaphragm pump with pulsation dampener is not that much expensive. Search for "metering pumps" or tell us where you are from and we can give you some vendors.

Installing a pulsation dampener at the peristaltic's discharge is still the cheapest solution to improve the situation. Keep that in mind.