Telco,
I hope you are being a bit facetious about not liking the LS, (and sticking a 6.2 in it). Granted,,, the car has it's quirks... but it's kinda like being married. You take the bad with the good,,, and hope she doesn't give up on you.
Ironically... from the research I've done,,, the new 365 HP 3.5L Ecoboost would fit in the LS. The only problem I see with that,,, is getting 2015 electronics to "play nice" with 2004 electronics. That's why I figured a decent upgrade on the 3.9 would be the all aluminum 4.6 from a similar year Aviator. My thought is most of the electronics would "play nice" with each other,,, with only some "pinout" changes in the connectors. Then you would have a 300HP/300 LB FT torque engine that would surprise a few people, (without the VVT issues).
I'm not looking for a Z06 or SRT killer,,, but something that will surprise a few modern cars of today. I've toyed with a few of them,,, and the LS is still no slouch in todays terms. I think Ford was on this right track years ago with the 4.6,,, but went overboard with the supercharger... and Jag sucking the life out of them. From what I have read,,, Jag killed the possibility of any HP version of the LS.