Dealing with Britons in Arena as Mongols

I only play Arena, and I only play Mongols, so please don't say to pick a different map or civ. For reference, I'm around 1300 ELO (DE) only playing this map/civ combo, so I'm not a crap player, but far from an all conquering god. Ranked game, so assume I'll be playing another 1300 player.

Now, I havent had any specific problems against any civs (i.e. I win some, I lose some) except when I face Britons, where my win rate is definetely sub 30%, and honestly I think it's more like 20%.

What generally happens is: we both go for a FC. I will put a defensive castle in my base, as typically one thinks that Mongols have a very strong late game, the difficulty is surviving their poor castle age. The Briton player will either do the same, or try to do a forward castle drop (which is just a standard thing to defend against that any civ can do, so no particular issues at this point).

My problem actually comes later, when typically, they start to spam arbalests, and I go mangudai. The arbs slaughter the mangudai owing to their vastly superior range. Onagers aren't a counter either because people will just micro their arbalests away and snipe your onagers - you'll never get a shot in against anyone halfway competent. Spamming hussars isn't great either as they lack the final pierce armour upgrade, and in practice get shredded by massed arbs. Those three unis (Mangs, Hussars, Siege) are basically the Mongol meta, and none seem to work all that well. The only times I seem to beat a Briton player is when it's very clear there's an imbalance in innate skill level or they make a terrible mistake like leaving their archers under castle fire for 15 seconds while they're paying attention to something else. Essentially, unless the opponent messes up big time, they win.

Any ideas on how to counter this? Castle age pushes with mongols before they get up to arbs doesn't seem like a good idea as Mongols have a poor castle age but a strong Imperial. But even our strong imperial units don't seem to fare that well against a ball of super long range arbs!