I don't know much about the G-DEC, but I do know the three essential components for that tone (aside from your playing technique) are a Super II pickup split in the middle position, a Blackface preamp scenario with good spring reverb, and JBL-E120 speakers.
If the G-DEC can use custom IR (impulse response) files, I can give you the E-120s. (Presumably, being a Fender product, it can do a convincing Blackface and you can probably dial up some good overdrive to go along with it.) But while I can get a convincing 87 tone with my AxeFX rig and Tiger guitar, it goes out the window without the Super II. I've tried the very same preset with my Suhr Strat and the middle pickup (a Suhr Vintage 60s single coil) just doesn't get "that" particular sound to it. Neither does my PRS with a split Dragon pickup, or my John Buscarino frankencaster with an EMG single in the middle. Adding EQ doesn't get it either. It's intrinsic to that Super II pickup, much the way getting an SRV tone can't really be done with a PAF, or Keith Richards without a Tele, etc. etc. etc.
It's also difficult to knock a specific tone with a modeling amp unless you happen to have the analog equipment set up and running to A-B with, which I did when I made my AxeFX preset. In fact, it was close enough where I sold off most of that gear.
All I can really say is, the working Tiger tone in the context of a band mix has more mids than you probably would think it does, and more reverb (which washes out later in the mix). The tendency when you are listening to the guitar on its own is to think treble is good, but when you try to fit that crispy sound into a band mix, it winds up being way too thin. Which goes a long way toward explaining why Garcia probably thought his direct Bolt tone sounded cool over his ear monitors every night, but it was thin and spidery in the recordings later.