I'm building some decks with only the Core Set plus all three deluxe expansions to see what types of archetypes are will be available permanently throughout Netrunner's lifecycle. I'll put "big boxes only" in the deck titles so they can all be retrieved via search.
The hardest part of building a Butchershop archetype with only the big boxes is finding enough economy to outpace the runner. The modern archetype has access to two great econ operations in Sweeps Week and Restructure which make it possible gain money quickly. The big boxes lack good econ operations, other than Hedge Fund, especially if all your influence is spent on meat damage.
This started out as a Spark deck but I turned to SYNC for a few reasons. While Spark aids you a little bit in your economy war with the runner, it does so at best 2 credits each pair of turns, and even that is tough to achieve with an optimal deck. SYNC turns Data Raven into an incredibly taxing piece of ICE, one which can quickly accrue more fiscal advantage than the Spark ID, while also having a smaller deck size which helps you find your combo pieces.
The agenda suite looks terrible without Project Beale or the economic swing agendas (Explode-a-palooza & NAPD Contract), but it's not too bad. Breaking News was always the best to grab a kill with Butchershop and now we can fit in 3. We reduce our density a bit with Global Food Initiative and fill in Private Security Force because nothing else fits.
We have a couple avenues to the meat damage kill:
Midseason Replacements isn't actually missed that bad, certainly not as much as the agendas and econ operations.
Launch Campaign accrues money a bit quicker than other drip and is neutral, so it's an auto-include. PAD Campaign takes a few turns to pay off but is hard to trash. Hopefully we can hit a Melange Mining Corp. for a turn or two at some point and our never-advance bluffs are strengthened by the threat of News Team, which is just brutal out of SYNC. Special Offer rounds out the last of our economy choices as a sort of Pop-up Window replacement.
As I noted in my Personal Evolution deck that's only core + big boxes, I'm not sure how to deal with agenda flood in a Jackson-less world and a fourth of this deck is agendas, plus it doesn't have space for Archived Memories which appears to be the best option in the big boxes. I guess you'll just have to protect Archives? Or kill the runner very quickly.