How to create and use many to many relationships with FastAPI and SQLModel and avoid circular references?

Question

I've got a Python 3.10.8 FastAPI application using SQLModel and having trouble with many-to-many relationships. I can define them okay using strings to refer to the class on the other side of the many. Here is a simplified sample of one side of the many-to-many schema/model:

schedule.py file

class Schedule(ScheduleBase, table=True):
    __tablename__ = "schedules"
    id: Optional[int] = Field(default=None, primary_key=True)
    plans: List["Plan"] = Relationship(back_populates="schedules", link_model=SchedulePlanLink)

Here's the other side of the many-to-many schema/model:

class Plan(PlanBase, table=True):
    __tablename__ = "plans"
    id: Optional[int] = Field(default=None, primary_key=True)
    schedules: List["Schedule"] = Relationship(back_populates="plans", link_model=SchedulePlanLink)

And here's the association table between them:

class SchedulePlanLink(SchedulePlanLinkBase, table=True):
    __tablename__ = "schedule_plan_links"
    schedule_id: Optional[int] = Field(
        default=None, primary_key=True, foreign_key="schedules.id"
    )
    plan_id: Optional[int] = Field(
        default=None, primary_key=True, foreign_key="plans.id"
    )

This works and creates the expected tables and FK's, etc. The problem arises when I try to access the data. I have a SQLModel class that looks like this:

class ScheduleReadWithPlans(ScheduleRead):

    plans: Optional[List["PlanRead"]] = []

And I have to have this in order to read the data and return it via a route:

ScheduleReadWithPlans.update_forward_refs()

And I can get the schedule data with the list of plans. But if I try the same thing with plan data trying to get a list of schedules (with the appropriate classes define), I end up getting circular references.

Any ideas about how to define/configure this kind of thing to to work?