Building a 340 engine

Eagle SIR rods are complete junk. I wouldnt run them lawn mower
Use anything else. Anything
Please elaborate!

500 hp is pretty high hp per cid especially for a daily driver. Plus the X heads are good for about 400 hp and eddies 450 hp unported, It takes a 360 ish size engine make peak hp about 500 hp @ 6500 rpm, 450 hp @ 5900 rpm, 400 hp @ 5200 rpm, 350 @ 4600 rpm.

Around 1 Hp per cid for most is about the best compromise for street friendly performance, for some 1.1 hp per cid, Above that your more into street strip territory.

I'd go with with Eddies and a high lift short duration hydraulic roller, kind of how new Hemi and LS make power all head flow with moderate cam.
I think 273 nailed this. I myself would opt for ether a solid flat tappet or roller. But it is hard to get a small roller and out perform a good solid lifter cam.

At 370 cubic inches, you’ll need 1.35 HP per cubic inch to make 500 HP. We are getting a little stout here.

The only thing I can suggest s to save up for the best cylinder head you can purchase. A serious full porting of the Edelbrock heads will be in order. You’ll need to work on the RPM-AG a bit as well (IMO) with gasket/port matching it and going as deep as possible. The capability of the intake really comes through with this work and (again, IMO) with 370 cubic inches, it will be a good pay off.

How heavy is the Dodge business coupe?