I'm not sure if this has been suggested before or if it is already planned (apologies if it has) but I think it would be cool if after reforming the WRE either as the Britannic Empire or the Gallic Empire you were given a decision to request that the ERE recognize you as the legitimate Western Emperor. Whether they accept or not could depend on a variety of things, like prestige, realm size, gender, religion, and gifts sent with your emissary (gold). If they accept you get a prestige bump and a small boost to vassal opinion and if they decline you get a large loss of prestige and a significant penalty to vassal opinion.
If the ERE does recognize you they could also involve themselves in succession wars, supporting one claimant of their choice with gold and troops (these troops could reflect either mercenaries hired by the ERE or soldiers convinced to fight for you because of your Eastern support). If the claimant not supported by the ERE wins they will have to send a large amount of gold to the ERE to regain recognition. There could also be events where the ERE has a succession crisis (I'm not sure how often the ERE had succession civil wars at this time but I would guess that they were fairly common) and if your empire is large enough you can provide gold to a claimant and hope that they win. If your claimant wins you receive gold and prestige from the ERE and if your claimant loses you lose prestige and have a lessened relationship with the new Eastern Emperor. This could all be reflected with an Eastern Relations stat that shows how good your relationship with the ERE is, with higher scores providing benefits and lower scores providing penalties.
I hope I didn't ramble too much in this post, but I hope you'll think about somehow developing this idea and integrating it into the mod. Also I'd like to thank all the creators of this mod, this is one of my favorite mods for CK2 and I hope you continue to work on it.