The little Denso alternator off of a GEO is 5.5 lbs and puts out 55 amps so something like that should work. I have some alternator bracket kits on my website or I'm sure you could fab something. I built a few alternator bracket kits from Ti once just for fun. It is fairly easy to do, just have a shop water jet out the brackets from Ti plate. A water jet cuts thru Ti fairly quickly.
One example on the engine is to take a serious look at the crankshaft. That Eagle crank you have might be stock Mopar journals or it might be BB Chevy journals. But you can go with SBC journals or even drop it all the way down to Honda journals to save weight. Carrillo makes steel rods for Mopar engines with Honda journals. Standard Super Stock type of parts. On the pin end you can go with a .927 pin rather than the typical .990 pin. Get a truss type piston with the short pin and you save even more weight. MM rings save weight, hollow lifters are lighter, beehive valve springs are lighter, etc. I sent my intake manifold to Wilson for porting recently. It came back 1.5 lbs lighter and I picked up 25 horsepower. There is weight that can come off the heads down in the pushrod area. Most of that webbing can be removed without causing any harm. You can have the camshaft gun drilled to save a little weight. Milodon makes an aluminum oil pump that is 3 lbs lighter than factory cast iron pump. The small oil filter from an Omni weighs less than the standard one and holds less oil.
Here is a picture of my rotating assembly. This crankshaft has been gun drilled, rod journals are drilled, the counterweights are machined out, the flywheel flange is profiled, etc. They took 14 lbs off of this crank and it could be even lighter with some more work. The connecting rods are SCAT I beam rods which are super lightweight. With Honda journals and .927 pins they would be even lighter. My pistons are shelf stock so they are a little heavy but piston vendors can make super light pistons if you ask.