That does make sense. My mistake on misreading your first post. I got the impression the loader was already back on and hooked up/
And mo, the loader valve is not properly plumbed. It may work the way it is now, but that doesn't make it right. It's obviously power beyond capable, it's even marked so. Two problems.
Problem one. You only have a pressure out and a pressure in port on the block under the remote valve. That's not the block I prefer to use. I like the one with three ports, one of which is a sump return. On the 4000 adding a sump return can be difficult. Those I'm aware of with that style block use the hydraulic fill port on the back for a sump dump. Makes it rather awkward when you need to add fluid you have to remove the return hose an fittings to get the port free in order to put oil in. With the right style block the sump port is right there.
I'm not saying you MUST do this, it's just another choice you get to make. If it's working today, it will probably still be working tomorrow, but there are down sides to operating it this way, In power beyond configuration, when using the loader the oil returning from the cylinder goes directly to sump through a relatively free flowing path. As it is now, that returning oil must go through the lift system first and then back into the sump. If you're carrying something on the lift, and operate the loader the oil in the system is performing double duty. If the lift settles just a bit the linkage directs oil flow to bring it back up to whatever position the levers are set for. When you use the loader and lift a load the return oil is also trying to raise the three point back to set point. Sometimes that works out okay, sometimes it doesn't. I've had to remedy that situation a few times before. You might take a few minutes to read through this, it may be easier for you to digest than my rambling.
The power beyond sleeve prevents subjecting the exhaust or return passages and spool seals of the control valve to back pressure.
crossmfg.com
Problem 2. The power beyond sleeve you need for your particular valve may or may not be easy to find, depending on what make and model valve it is/ The old Gresen valves (if that's what you have) were very common at one time, and many are still in use today. Now owned by Parker, the sleeve Parker supplies for some of them are outrageous in price.
As for the single acting valve, I won't swear to this, but I think the knob on the front of it when backed out a few turns will allow the valve to operate in double acting mode. You would need to remove the plug on top and add a fitting and another hose. I THINK that may be the case. There were a number of different valves used on those tractors, not all were identical in operation.