With the EU level:
government proposes legislation in the Council -> Council passes it -> [lots of steps within the EU...] -> directive comes to Swedish parliament ...

...

Mixing in the executive governments as the strongest part of an EU-level legislative process shifts power nationally to executive governments, weakening what checks existed on the national level.

This is inaccurate. First of all, the Council is not the strongest part of the EU legislative process, nor does it propose legislation. Legislative initiative is with the European Commission.

What national governments do is introduce amendments to proposed directives during the codecision process (subject to European Parliament approval), and (in secret and behind the scenes) collude with one another and with the Commission to have new directives or regulations introduced that would be unpopular at home.

We have met the enemy, and it is us — Pogo