Sweet! As a guy who grew up in the '80s, I salute you!
A few suggestions, purely my own ideas. Ideally, I hear a huge, gushy John Sykes-like tone over this. I also agree about cutting out some of the presence and accentuating the low mids. You really want this to sing. Don't be afraid to work with a little more gain and using the bridge pickup if you rerecord the lead part--this would help get a little more sustain while still being sharp.
Also, to make the guitar sound big while still fitting in with the backing track, you might try lengthening the delay time while also cutting down on the percentage mix of the delay. The initial effect will be to make the guitar seem a bit dryer and more forward, but then the key is to add a whole bunch of beautiful Whitesnake-level reverb to the entire mix. Lengthening the delay time adds "eyebrows" to the delay effect, and the dryer delay mix preserves the original line a little better. Once you do that, you might be able to bring the lead part down a little bit in the mix, and make it all fit with a bunch of reverb. Trust me, it'll be like spraying your hair with an entire can of Aquanet.