Indexing and joining JSON data in Postgres - json

Question

We have a table of data that looks like:
CREATE TABLE objects (
id BIGSERIAL NOT NULL,
typeid BIGINT NOT NULL,
fullobject JSON,
PRIMARY KEY (id),
...
);
and
CREATE TABLE types (
id BIGSERIAL NOT NULL,
type VARCHAR(255),
PRIMARY KEY (id),
...
);
in the objects.fullobject column is JSON data for users and orgs like:
// id: 1
{
...
"type":"1", // user
"orgs":[
{"id":"2", "position":"foo"},
{"id":"2", "position":"bar"},
{"id":"3", "position":"foo"},
]
}
// id: 2
{
...
"type":"2", // org
"name":"Org 1"
}
// id: 3
{
...
"type":"2", // org
"name":"Org 2"
}
The question is, if I want to find a user based on the name of the organisation, how do I do the join?
I'm not sure if I can create the right index on the org data inside a user.
The two solutions I can think of are:
Create a single text attribute that contains the id's of the orgs for a user, then do a join based of that (e.g. "searchableOrg": "|org1|org2|").
Then the query looks like:
SELECT * from objects user
INNER JOIN types usertype ON usertype.id = user.typeid
INNER JOIN objects org ON json_extract_path(user.fullobject, 'searchableOrg') LIKE '%|' || org.id || '|%'
INNER JOIN types usertype ON usertype.id = user.typeid
WHERE json_extract_path(org.fullobject, 'name') LIKE '%whatever%'
AND usertype.type = 'user'
AND orgtype.type = 'org'
Here I can have indexes on json_extract_path(user.fullobject, 'searchableOrg') and json_extract_path(org.fullobject, 'name').
However this doesn't work if we add things like a start or end date to the user's organisation membership and need to further filter the join on that.
Create a trigger that when a user is created/update/deleted modifies a table (userorgtable) that contains the user org membership and do the join off of that.
I haven't looked at triggers yet, but hopefully the query would be something like:
SELECT * from objects user
INNER JOIN userorgtable userorg ON user.id = userorg.userid
INNER JOIN types usertype ON usertype.id = user.typeid
INNER JOIN objects org ON userorg.orgid = org.id
INNER JOIN types orgtype ON orgtype.id = org.typeid
WHERE json_extract_path(org.fullobject, 'name') LIKE '%whatever%'
AND usertype.type = 'user'
AND orgtype.type = 'org'
In this case, if we needed to add further attributes to the join (such as start and end dates), we can just put them in the userorgtable and have add conditions like:
AND userorg.startdate < CURRENT_DATE()
Is there another option? Perhaps using more of the Postgres JSON functions?
Thanks in advance