Really to get the Clans to win you'd have to change them so much they'd not be the Clans we know and love. You'd actually have to give them a sense of grand strategy, have them work together instead of it being some kind of race more akin to this
https://www.youtube.com/watch?v=nOQ89oRj3U8You'd need to have the scientists supporting the warriors instead of thinking they are a bunch of knuckle dragging jocks who can't be trusted with shiny things so give them some more advanced tech (as well as them being less conservative) so the Clans also turn up with things like the HAG, HL and ATM in addition to their normal kit (possibly ER Pulse and SLRMs on very new prototypes).
You'd need the Clans to listen to the Grand Council rather than it just be a chamber where people can insult one another whilst the Loremaster goes grey trying to control the yelling and threats of violence. They'd need to be more unified, yes have the divide between Crusader and Warden but when the Grand Council and IlKhan say something then that is it.
You'd also have to probably have the Clans be considerably larger in terms of military forces, not only in terms of mech/elemental forces but also having a more combined arms strategy and a grasp of things like logistics instead of having the concept of Logistics that would worry even Rommel. Their front line forces would need to include tanks, infantry and mechs as a unified whole (you know like the SLDF use to...)
This larger number of forces (along with ALL the clans invading when the invasion starts with them working together, not the Silly Olympics) would allow them to absorb losses rather than acting like the Imperial Japanese Navy and Airforce in WW2 being ground down to uselessness in Guadacanal.
And these are just things I can think of off the top of my head, I'm sure there's so much more that the Clans would need to do for the Invasion to succeed.