OK, looked at the pics, and read everything. Making some assumptiuons here about the pump in that the actual 3.7 GPM rating is at 1000 RPM. making those assumptions here's my next observations and suggestions.
Looking at the pic you've got the sprocket sizes backwards (ie the larger one on the engine and the smaller on the pump) so your actually speeding up the pump. That said I'd think you'd want to run the engine well above an idle so it has power to dump the trailer when it's loaded and the highest hydraulic pressure is needed. To do that requires nothing more than some simple math. If you want to run the engine at 2000 RPM and the pump at 1000 then you need two sprockets with one having twice as many teeth as the other. This would turn the pump at 1000 RPM and, assuming the 3.7 gallons is at 1000 RPM, would net you right at 3.7 gallons of flow.
Now, to slow the pump down, and reduce your flow, all you need to do is use spockets with an even larger tooth count difference. If you were to put a 25 tooth sprocket on the engine and a 5 tooth sprocket on the pump with the engine at 2000 RPM the pump would turn at one fifth of it's usual speed, or 200 RPM. This, in theory, would give you a pump flow of about .7 GPM. If that isn't enough flow you can go with say a 20 tooth sprocket and a 5 tooth sprocket. This would change to the ratio to 4-to-1 which would turn the pump at 250 RPM and give you a flow of .925 GPM. Using the 4 to one ratio if you sped the engine up to 3600 RPM than it would give you a pump speed of 900 RPM, and should give you a flow of about 3.33 GPM. By the same token with the engine at 2000 RPM it would also allow you to slow the engine down some and reduce the flow from the pump wto well under a gallon a minute.
That all said, for the cost of two sprockets you should be able to get your flow rate down low enough to meet your needs and still keep the engine at a high enough RPM for the engine to do it's job properly, and also give you wome wiggle room to control the flow with the throttle to nearly it's maximum. That's a close estimate on taking care of the problem using just two different sprickets. Beyond that you can play with sprocket sizes, if you want, to achieve the optimal engine speed and flow rate compatible with your needs.
Granted I understand your wanting to make the thing using all parts you have lying around, BTDT many times myself. Unfortunately there are times when it is cheaper and easier to buy the critical parts needed to make the thing RIGHT, than it is to use will fit parts and then have to buy another, more expensive part, to make sure the will fits actually do fit. Good luck.
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