13 sec. 360 for $3,000?

How would you build a 360LA with the following restrictions and with a goal of a mid to low 13 second street car at 3600lbs

- Stock bore, and stroke (and pistons preferably too)
- 3.00 rear axle ratio
- must run on pump gas (87 octane preferably, but 91 is an option)
- max budget of 3k for engine and converter (727)
- ability to retain power steering and brakes (brakes not a MUST, but would be nice)

I have a lot of LA parts kicking around already (gaskets, bearings, ignition, trans, carb, etc) and have done a low budget build like this before, but not on a vehicle this heavy, nor with this kind of gear ratio restriction. Trying to do it on a budget, so going to try and piece what i dont have together using second hand parts.

So, how would you do it? Or have you actually done it?
I'd put aside the low 13's goal, if rebuilding the engine I'd make sure the short block was done right with good pistons anything else could easily changed down the road. If money left for a good stall would be my second main purchased. I think I'd like the journey of mod to mod improvements and working my way there.

318willrun has shown what can be done with very little, and you could go with a lot more cam than his before powerbrakes are an issuse.