Any suggestions on an infusion resin for fiberglass? (Preferably something that cures very slowly?)

I'm working on a trunk lid for my car. It's about 3.5' x 4.5'. I'm pretty sure the normal polyester resin is going to cure well before it saturates the fabric.

You should be able to infuse a part that size using most common infusion resins.  The key will be in the flow-media you use and the feed setup.  I've seen simple parts that size with a low viscosity polyester resin fill in a matter of minutes.  Epoxy will be slower because it generally has higher viscosity, but you have more time with epoxy. 

You want something under 250cps or so - but most resins sold specifically for infusion be thinner at a reasonable room temperature.  What you use depends on where you are in the world and what you can get easily.  For large panels that need to be thick enough for stiffness but not super light, look into a core/flow media like Lantor Soric.