Im going to share two cam builds that I have done with a zz4 and a 383 that should give you extra power to achieve your 11.99 to 11.50 time slip.
This would be just a cam and intake swap. The cam is a UDHarold suggestion for a street 350 and 383. Harold recommended it for my zz4 and my Dads 383. We both have similar heads to you...so the heads are a wash. The intake should boost your mid range torque as well.
From my research the zz383 has a-12 dished piston in it....which puts you in great shape.
I would pull your engine and get the top end off and the cam out. Here is the cam I would purchase directly from Luanti.
Street Master Retro-Fit Hydraulic Roller Cam - Chevrolet Small Block 280/288 - Lunati Power
The cam comes on a 112 lsa. I would get it cut on a 110 or 108 LSA and if you have a step nose cam in the zz383 you can get that cut on the cam as well. You are going to have a higher DCR with either a 110 or 108 LSA. You should be ok with a good tune and cooling system. Like I have said, I have ran this combo in a zz4 and 383 with no problems. If you run the 108 LSA your DCR will be around 8.4 and if you run the 110 LSA it would be around 8.3. This should give you a cranking compression of around 195 to 215 psi.
Once you have the deck clean and the cam and lifters installed, I would reinstall the Fast Burns with the Fel Pro 1094 as your head gasket. This shim gasket should raise your compression to around 10.5 to 1. The 1094 is a shim gasket with a 4.16 bore and .015 thickness...should give you a nice tight quench as well. I would run a 160* thermostat....this should help keep the engine running at 180*. Ours runs this in the hot Florida summers.
I would top the heads off with the Edelbrock Air Gap. This intake will give you more meat in the mid range, where you need it, than the single plane. If you run a one inch spacer on the Air Gap, you should be within a few horsepower of the single plane too. I have ran both of these and found this true. Since you trap at 5000 you will benefit from the extra torque of the dual plane. Hood clearance can be close with the space, but it does work in a 67 Chevelle.
This combo will need a great timing curve, something like this. Initial of 16* to 18*and a mechanical curve of 16* to 18*. Your total will probably be 34*. Your advance can should be around 12* and should give you a idle of 30*. Your cruise should be around 46*. This is a conservative curve and you could use more timing from the advance can, but its not worth it to me.
Ours is topped off with a Holley 3310. Your fuel injection set up should yield a few more ponies.
My Dad drives his car and does not race it. His 383 breaks the tires loose at a roll with his M20. He runs a 3:55 gear and a 255 60 rear tire. He drives it do errands and to the golf course. We have not had it on the dyno either so we don't know the exact rpm redline of the this cam combo in a 383, but we think its 5800 to 6300 somewhere in there. Now my Dad does run the 112 LSA, because he did not want the low speed bucking with the 4 speed.
IF you have any questions about this combo or cam and or the tune...just let me know.
If you spend money on the Luanti cam, lifters, pushrods, roller rockers if you need them and hardware you probably will be out 1000 to 1500.
Then all your going to need is a Air Gap and a custom converter....based on the new cams print out off the chassis dyno. This will cost you another 1300. So you will be over your budget some.
I feel doing something similar will help you get your 11.99 to 11.50 time slip.