I have been commuting across town from the Westside to downtown by bike for over 30 years. I have a possible solution to the vexing question of how to include a crosstown bike path and not remove parking on Micheltorena.
I realize that Sola is being considered as an option. Here is another idea:
Create a one-way street on Micheltorena from Castillo to State, and on Arrellaga, one-way from State to 101. Stripe them like Castillo and Bath, allowing for parking on both sides and one bike lane striped in.