You keep saying that the weight difference is huge. That's just not true.
2003 Evo 8 is 3262 lbs.
2003 cobra termi is 3665 lbs.
That's a 400 lb difference.
As for power for mods, do you realize that changing the pulley on the stock Eaton to a 2.93 takes the Cobra from 8 psi to 12 psi? And with the 2.8 pulley, intake, and exhaust you jump up to 470-480 rwhp? Mustang parts are cheap, and you still have plenty of mod money left from $5k. Slicks, IRS brace, and up the fuel and boost some more.
