Even with max Social skills trained, it seems like standing grinding is slow-going for the Alphas. Remember that you're not concerned with corp standing here, but *faction* standing. Once your standing with the Caldari State is above certain levels, you will be able to take missions with any corporation:

Level 1: Any standings
Level 2: 1.0 or higher
Level 3: 3.0 or higher
Level 4: 5.0 or higher

Also, bear in mind that Slav2 recommended those corporations because they are not farmed very much (as opposed to Caldari Navy, for example), and have a better ISK/LP rate and are thus more profitable. It might be prudent to let it use all Caldari corporations so you can do as many as possible until you can do L4's. You can do this by making sure your Home Station is Caldari and not using Selected Corporations.

Ah thank you !
Do you also tick "level home corp....." ?

Yes, but that's only because I turn my couriers into Traders, where that standing matters a lot for the broker fee. Otherwise, I wouldn't because my home station's LP isn't worth very much.

FAQ answered all my questions

Good!

If you tick "Level corporation standing" you will not make any storyline missions, but from home station corporation only. This is required if you faction standing maxed, but corp standing is not yet leveled.

Use alternative option to cancel offered encounter missions in they belong to home corporation: tick "Home Station Corporation Only" and untick "Level corporation standing". One of my couriers has 7.6 faction and 6.4 corp standing with this setup. Running 8h/day for 46 days.