This pic is of the remains of an Allstyle box coil. You can see the "stains" if you will of the A coil on the inside of the pan. Now this is an entirely individual piece from what your air handler is as yours has the coil inside of one big cabinet with the blower, but this is the best pic I have to show you how a horizontal coil and pan should look. Now on yours the coil will remain in the same position and again, you'd need a bracket that holds the coil in place. That bracket probably came with the original unit and might be in there or discarded since used as an upflow.
If you get the right pan for your unit (best bet would be to track down the manufacturer and make sure that you can use that as a horizontal first and then if so they'll be able to get you a pan but be warned, they are not less than $100. At least last time I was told for myself when I needed a drain pan for a similar situation it was going cost a near $150.00.
Anyways, call the manufacturer, give them the model and serial number to your air handler and they'll tell you for certain if it can be turned horizontally or not and if so, they'll have the pan specific to the unit. No spillage.