Did you type that backwards?(You said Starts slow then increases)
Im used to Starts fast then decreases
Water regulators come in several types
3/4 inch cylinder (About) no fancy grip on female end: JUNK
3/4 inch cylinder (About) w/ fancy grip on female end of wings.. JUNK
The one pictured above: Minimum I would consider, but I think it's a tad small
Sur-Flo (This is the one often factory installed) Minimum I would consdier
Watts, Zurin or other make at least 1/2 inch (Mine are 3/4) with hose adapters
EXCELLENT
Valterra adjustable: I have not tested but others are happy with it.