While the primary part of the question was answered by @wildplasser I thought I would put the entire answer for people looking at porting MySQL data to Postgres.
After trying out multiple solutions, the easiest and quite smooth solution was this: https://github.com/lanyrd/mysql-postgresql-converter
This worked quite smoothly. But just one problem- it does not port any of Mysql sequences to Postgres. This means if you have auto-increment primary ids, you will have to change your Postgres schema separately and create serial sequences after the porting is done. Apart from that, it was quite smooth.
To talk about the permission issue, logging in as Postgres user and trying to access dump created by original user failed, the right way to do it was stay logged in as original user and use postgres user only for DB operation by using -U postgresuser command.
E.g.: psql -U postgres databasename < data_base_dump
While for many this must be the obvious way of doing it, I must admit it was one of those eureka moments for me :)