We started to approach code reviews as engineering tasks, and it improved greatly our daily workflow

Hi!
I'm managing a team (around 6 devs, ~200 devs in the entire company) and we recently had some problems with code reviews and specifically collaboration between team members on reviews.

The way it used to work was as follows – someone would throw their merge request in the team's channel, and then start pinging team members for reviews.
This works eventually, but it keeps the dev blocked until someone takes a look at his code; moreover, some MRs are forgotten about/lost in the channel – until the dev remembers them and resends them again.

We started with a new pilot – sending a general Slack message before our daily standup and assigning each team member to an MR he should review; so far it's working much better, and team members are integrating reviews into their workflow.
Has anyone experienced anything similar? would appreciate some extra tips to reduce the time it takes to merge code/improve collaboration.
Thanks!
(Full disclosure – I'm building a tool that originated as a solution for this exact problem; super curious about how different teams approach and solve this issue )