it would be easiest to just swap the lines at the carriage. You would have to make up new hoses but in alot of cases the lines at the control valve are pre-formed steel lines for the attachment functions and cannot be moved. If the lines in the carriage are steel tubing than that would make moving them at the carriage difficult also.
If this is not the case then you might be able to move the lines at the control valve, or possibly move the connections around at the bulkhead junctions at the front between the mast and frame, but that might be limited due to how the hoses are ran into the mast array and not the best option.

Without knowing the exact configuration you have there it is hard to give good advise on how to switch the functions. You'll just have to figure out the best point to switch the lines around.

As for as relieving pressure before disconnecting lines?
if this truck has the operator presence system and has solenoids on the control valve then just turn on the key, activate the seat switch, do not start the engine, pull on the levers and this should release any pressure on the lines.
If just a standard hydraulic system (old style) just pull the levers in both directions and it should release the pressure.

You have quick disconnects on the carriage?
Is the push/pull set up so you can have it on when you need it and remove it for when you don't?
I was under the impression that you understood that the "swapping around" of the hoses would need to be done at the hydraulic control valve.

We took it outside and unhooked the quick connects. Nothing came out but we realized that of the 2 hoses on each side one has a male end and the other has a female so you can't just switch them over. I am out of ideas at the moment.

The only step I can think of is to be sure you get everything positioned like you want it (side shifter centered, push/pull drawn all the way in toward carriage). Then while you sit in the seat with key switch on, but engine not running..........operate both the side shift function lever and the push/pull function lever several times, operating the levers fully in both directions. This will allow any "pent up" residual pressure in the cylinders of both devices to bleed off internally back to the truck hydraulic tank.
Then turn off the key when you get that done.
But you are still going to lose a little oil from the hoses.
Make sure you mark all the hoses that have to be removed so you don't have to do a bunch of tracing later if something gets mixed up.