That's not a bad move, but the cost is high and the payoff is only moderate. Against a Str 20 Paladin, he's got a 62% chance of success per contest (assuming Blur instead of Foresight). Against a Str 16 Paladin, 70% chance of success per contest (w/ Blur). If he uses both attacks to grapple/prone the paladin, he has a 49% chance of having a grappled/prone paladin at the end of his turn**, which will raise his chances of hitting at least once on his following turn from 1% up to around 10%. The Storm Giant has improved his physical attacks from "totally futile" to merely "hopelessly outclassed."
If the Paladin is using Foresight as mentioned originally instead of Quickened Blur, it's even worse. Odds go down to 56%^2 = 31% against the Str 16 Paladin, or 46% = 21% against the Str 20 Paladin. That's practically back in the "totally futile" bucket.
Yes, Levitate and Lightning Strike are better, but if you have to give up on physical attacks and switch to magic, that means you've already conceded the point about AC.
** I'm sure you know that technically, it is illegal for a RAW Storm Giant to grapple/prone in the same turn, because it doesn't have Extra Attack. (Multiattack only specifically allows you to make two Greatsword attacks--not two grapples, or a grapple and a push, or two boulders, or anything else. Only two greatsword attacks.) I think most DMs including myself would ignore that technicality and allow the Storm Giant to grapple/prone as if it did have two attacks, but it would technically be a customization.
1. Yes I know that RAW ruling and it's one of the more stupid ones, so I ignore that.
2. Okay wait, stop.
In what world is he facing a SINGLE Storm Giant (CR 13) when someone in the party has access to Foresight, a level 9 spell??? Level 17 characters would be facing 10+ Storm Giants to even be a moderate fight, in which case those Lighting Bolts will fry the Paladin before anything else happens.
3. You had the Paladin casting Blur. That means the Paladin is concentrating on it. Lightning Strike (if the Paladin fails the Dex save it is statistically likely to fail) means a DC 27 Con save to maintain concentration. Even with Aura + Resiliency (Con) that's terribly unlikely. So round 1, the Paladin's Blur goes poof.
4. I'm sorry, but the question wasn't how to beat the AC of the Paladin. I couldn't care less that I'm "switching" to spell casting. Hell the Paladin itself in your build has to rely on spell casting (Blur/Foresight) so why wouldn't the enemy? The OP wanted to know how to deal with high AC/decent save characters like the Paladin. The answer is almost always going to be creative spell casting (Dispel Magic, Heat Metal, save or half damage to break concentration, etc.) or Grapple mechanics that ignore both AC and Saves.