I have tried a Gold and Diamond uprade cards in the upgrade slots on the Flux Compactors and it will adjust the tick rate, but then will say "Inventory is Full" and will no longer output items when connected to Basic Logistical Transporter's from Mekanism

That sounds like the pipe does not have a big enough inventory to hold all the output. You can either try upgrading the pipe, or output to a chest or other inventory first.