What would your part list be... on as low a budget as safety would allow... to be able to rev a currently STOCK lt1 block to 6800rpm?

 

Cheap and reliable don't often go together. Where the weakness of a stock bottome end is found is on the caps of both the mains and rods, mostly the rods and tight bearing clearances. The bearings will catch and spin and under higher revolutions it is more than likely.
To clear that problem up some, most engine builders open up the bearing clearnces a tad and use quality fastener's, I can't think of one any better than ARP myself. Good machining also plays a vital role in longevity so shell out the extra 150-200 to have it align bored/honed on both the mains and cam bearings.
I also recommend using forged components as the price variance isn't that much a difference for the added insurance of having more durable parts under the most extreme conditions. Even a "budget" built LT1 can be pricey the choice is yours however, do it for 3/4 of the cost now, or pay double for it later

 

Why does the motor need to spin 6800 rpm? Maybe the better thing here would be to discuss what you want the car to do besides spin 6800rpm. Anyway heres a short rundown of what I would do.

Keep your stock crank, the stock rods would be ok/marginal with some good arp bolts. Honestly though on the rods I would look at some cheap scat I beams with 7/16" cap screws. I would be a little nervous about taking a stock type hyper piston that high but its been done. That said the cheap forged pistons are going to be very heavy and expensive to balance. Your money will be better spent on just getting lighter/better pistons from the start, the mahle powerpack stuff is goof for n/a apps.

When you have the block machined have it line honed using main studs torqued to spec. Make sure they use a tq plate to hone the cylinders and finish them to the ring manufacturers spec for Ra and Rz. Tap the oil galleys behind the timing chain for screw in plugs instead of the cup plugs most use saw one blow out when I was younger and tore up holy hell. I like to drill a .030 hole in each of the side ones to lube the chain, some dont but there are no negative effects. You will also want a very nice high quality damper, I personally prefer ati.

Buy good quality bearings and if you dont have the proper tools to check clearance let the machine shop do it. I like to set the clearance in the middle or slightly loose end of factory spec. Use a stock vol pump with high pressure spring. Using 10w30 or 40 I usually see about 40psi idle and about 70psi wide open. I do a few mods to the oiling drainback on my stuff in case of a valvetrain failure to keep parts out of the shortblock, and keep the oil draining where I want it to.

All that said, your biggest expense here is going to be cylinder heads and a cam/valvetrain to actually run to 6800 rpm. I have also found that the opti likes to explode at these levels.