Looking back a bit, increasing the strength is all but demanded. Dragon Slayers have a innate +40% against Dragons, but Monstrous they already get a +25% against melee, which matches even the best weapon strength increase.
With Mithril, a dragon slayer has a base strength 10. With a +40% strength against Dragons, it has base strength of 14, or +4. You get it combat 1-5, it has +140%, or 24. A nice, respectable number.
Coatlann the Wyvern, the weakest of the dragons with a base strength of 20 and a +25% against Melee also has a +4, for 24. No other promotions. A fresh-off-the-line Coatlann not only has the same strength as a full combat-line promoted Dragon Slayer, it has built-in first strikes.
Now, that's fair enough for a real dragon: a stack of Dragon Slayers is appropriate, albeit it should be a much smaller stack than any other nation's champions. (Built-in-courage helps.)
But Catlann is one of the weakest Monstrous creatures. Eurabatres, with a base strength of 50, gets 12.5 strength advantage against a Dragon Slayer. That's more strength than an Iron-weilding dragonslayer starts with, and that's all bonus.
Now, for most other Melee line, I could sort of understand this. You're supposed to focus on archers and seige weapons to take these down. Cool, I rarely see the point of going down the archery line very far.
But these are Dragon Slayers. As in, their job title is supposed to be what they do best. They're not 'merely' supposed to be better than other Melee in a one-sided annihalation, they're supposed to be super effective in their trade. Better than archers or catapults even: these are supposed to be swordsmen who can climb into a Dragon's own lair, challenge the dragon, and have a real chance to win.
Dragon Slayer promotion might need a tune up, sure, but there needs to be more than that. Dragon Slayers at the very least definitely need to be retrofitted to be good against Monstrous Creatures.