Does Jayce Man of Progress account for cost reduction (eg: from Ornn's Forge BF), allowing you to bypass the 7 cost limit after you killed another gear?

No — cost reduction doesn't widen Jayce's eligibility. His ability checks the gear's printed Energy cost ("a gear with Energy cost no more than [7]"), and any effect that needs to determine a card's cost for a purpose always uses its printed or copied cost, even if it's being increased, decreased, or ignored (Rule 206). So reducing a gear's cost with Ornn's Forge (or anything else) never turns a printed 8+ Energy gear into a legal choice.

Paired with that, Jayce already ignores the chosen gear's Energy cost entirely, so Ornn's Forge's [1] discount has nothing left to do on that play — you'd still owe its Power cost either way. Ornn's Forge's discount is only relevant when you're actually paying the Energy for a gear, not for Jayce's "ignoring its Energy cost" play.