There are 3 code HH's that show up on the nastyZ28 site.....

HH 1965 327 s h/p, m/t 365 4 Vette (Special High Performance, Manual transmission, 365 hp, 4-bbl carb, Corvette)
HH 1966 327 air inj. reactor 300 4 Vette (First of the emissions devices, 300 hp, 4-barrel, Corvette)
HH 1969 350 tur 400 300 4 full size (Turbo 400 auto trans, 300 hp, 4-barrel carb, engine used in full size car)

The heads are nothing special, so I'd bet this was, as Dave said, a run of the mill 300 hp motor. If the heads need anything more than a couple hundred dollars worth of work, there are other heads out there that will work better. You know first thing that you have to put hard seats in the heads. And I don't know or not if they are drilled on the front for bolt-on accessories. The guides may be worn out or the valves may be trashed. You know the springs are junk. And then, what does a good valve job cost in your area. In the end, I can see you spending around $700 to $800 to freshen these heads and you will still have a set of ho-hum production heads.

What I might be thinking to myself is that I bought a block and a set of rods. I think I'd install ARP rod bolts in the rods and have them re-sized. Then I'd ask the machinist if he had any 350 cranks laying around. I'd buy a set of pistons with a 1.560" compression height and have the machinist cut the block decks to zero piston deck height.

I'd call up Milodon and order up a 7-quart pan, good pump, windage tray and crank scraper. That would put the short block together. Now, share with us the other information that Dave asked for and we'll make up the long block.