For Axi/Neo, the most consistent way is actually 4 wave Interception. Eris, Xini is the current popular place but you can do Sedna, Berehynia too. The problem with Hieracon and other high level Excavation missions is that Axi/Neo relics only drop on B and C and with a 42% for a Neo and 77% for an Axi. On interception, Neo drops on A with 66% chance and Axi on BC with 100% chance.
You can do Extractors faster, but this is only true if you can handle 2 at a time (trigger them as fast as they spawn) and most groups can't consistently do double Extractors at the 30-40 level. For Lith Extraction is better (Earth, Tikal) because a single player can handle an Extractor.
For Meso, the midrange defense missions have a 85% chance to drop them on A. The strat is to do two waves then leave. The missions are Jupiter,Io; Saturn, Helene; Sedna, Camenae; Europa, Paimon. I like Helene the most because Saturn drops Orokin Cells.
I don't know what the economy is like on consoles but it's really most efficient to only run Neo/Axi relics. A Nekros Prime Systems sells for 150p. BP is 100p. Chassis is 14p. Neuroptics 70p. Rather than spend time grinding Lith and Meso, you can just keep going for the Systems and BPs and sell those, then buy Chassis/Neuroptics. A lot of Galatine Prime parts also come from Neo so you get to fill out those parts (or sell them) while grinding Nekros Prime.