In recent years, there has been a considerable push towards ultrahigh dose rates in proton therapy to effectively utilize motion mitigation strategies and potentially increase the sparing of healthy tissue through the so-called FLASH effect. However, in cyclotron-based proton therapy facilities, it is difficult to reach ultrahigh dose rates for low-energy beams. The main reason for this lies in the large momentum spread that such beams have after reducing their energy to levels required for proton therapy, incurring large losses in conventionally used momentum or energy selection slits. Here we propose momentum cooling by using a wedge in the energy selection system (instead of a slit) to reduce the momentum spread of the beam without introducing substantial beam losses. We demonstrate this concept in our eye treatment beamline and obtain a factor of two higher transmission, which could eventually halve the treatment delivery time. Furthermore, we show that with a gantry design incorporating this feature, we can achieve almost a factor of 100 higher transmission for a 70 MeV beam compared with conventional cyclotron-based facilities. This concept could enhance the potential of proton therapy by opening up possibilities of treating new indications and reducing the cost.