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.
Cars exiting 101 at Arrellaga can turn right on Castillo and head toward Carrillo or turn left on Micheltorena toward State. Bikes heading back to the Westside take Arrellaga and turn left on Castillo.
A striped bike lane next to parked cars is not completely safe as I have been sent sprawling to the street from an opening door on a parked car, but it is a step in the right direction.