How can I replace the plywood under my air handler?
You've got a fairly sizable amount of extra refrigerant line. Lifting your air handler a couple of inches will not be a problem.

The only part I would worry about is where the lines attach to the air handler. That's where the tightest bend radius is and you don't want to get that any tighter. But since you're going up, that should actually improve that bend radius.

You should be able to find the weight of the air handler by doing a search for the specs online. Find the model number and drop it in to Google. In general, they don't weigh too much; two grown men can comfortably lift a fully assembled unit.

One thing you might consider is to leave your air handler permanently suspended. But instead of 2x4s, get 2 heavy pieces of angle iron about 8 inches longer than the width of your air handler, 4 threaded rods, and appropriate nuts/bolts/washers. You can also get rubber bushings to put on the threaded rods to damp the vibrations from your air handler.

Slide the angle iron under the air handler where the wooden blocks are that currently hold up your air handler. Attach the threaded rod to the angle iron. There's two different ways to do that. One is to drill a hole in the angle iron but that might be difficult because of how hard iron is. The other is to use u bolts. If you go the u bolt route, you need to attach it carefully to the threaded rod so it can't slip out. Don't rely on compression to hold it. . A good plan would be 2 nuts with a lock washer in between and 4 or more large washers stacked on top. That will prevent the u bolt from sliding off the end. 

To attach the other end of the threaded rod to your trusses, I suggest two 2x4s or 2x6s running perpendicular to the trusses the full length of the air handler, plus an additional truss bay on either side (this will spread the load across more trusses). Lag bolt the 2x4/6s to the trusses. Drill through the 2x4/6s for the threaded rods.

Here's a marked-up copy of your picture showing where everything goes. I outlined your air handler in black and grey (the grey is the hidden edges). The threaded rod is green and the angle iron is blue.