On another forum, a kind fellow suggested to me that I'm viewing the roll of my cavalry wrong.

Instead of treating them as super-skirmishers, I need to view them as super-manueverable fighters.

Towards that end, I'm equipping them with throwing spears in addition to their javelins.  The throwing spears allow them to re-roll any failed attacks in the first round of combat, which gives them better odds of getting first blood, especially since they are so crazy maneuverable that I can generally choose when and where a melee will happen.  Of course, "Fury of the Norse" might prevent me from charging them, though I'll make sure to have some higher-ranking leaders leading the charge to help with that.

Against Normans, if I can get a flank charge in on their knights, I'll get 6 attacks, re-rolling misses, before they respond with at most 2 attacks and no rank bonus.  Statistically, I can expect 1 kill from that attack, so all things being equal, I have a 50:50 chance of winning the combat now, which is better than "no chance".

For my infantry, the guy suggested focusing on archers, skirmishers and crossbow men.  Well, I can't have that many crossbow, so I need more archers.  I'll keep some spearmen just to have a slightly solid line, but they'll be my fighters of last resort.

So, here's my new plan:

• Bribe them or make friends with them if they're too strong
• Swarm them with el-cheapo foot skirmishers to confound their movement
• Pelt them with arrows and bolts the whole time to wear them down
• Race around their flanks with my Jinetes, and charge home
• Let my nobles lead the charge, pretending they're Alexander's Companions.
• Use my spear blocks to buy some time to cover any fallbacks