Quizzes sacrifice the quality time students can spend online, even though they are convenient for both the instructor and students.
The use of more informal assessments like self reflection, surveys, and group projects offer much more satisfying ways to use online moments and at the same time will maintain the depth of critical thinking and evaluation needed for retention of course content.
If you are looking for some new ideas to replace some of your one line quiz assessments -Look ME Up!
I've been moving some content online and developing new content that works better online simultaneously. I do all my quizzes and tests online now, even for face-to-face classes. The tools are just so much better than paper.
When I do weekly quizzes, I've been using them as a way to prompt the students to read the text more deeply. The quizzes are open book and due about the time start discussing a topic in our f2f sessions. I've been finding that the students are way more ready to discuss the content then. This has been making for better sessions where we work at a higher level, rather than just me lecturing on new content. I've been able to better use the time to enhance their understanding of challenging parts of concept application.
You make a great point for front loading the curriculum in any classroom situation. In front loading, you are supplying the students with the prior knowledge they need to comprehend the bulk of the material in a more successful, and as you point out, deeper way. In addition, you are using best practice for hybrid classes, which is to intertwine the content students get on line with the content they receive during f2f. One more point to celebrate is that in your case, you are mainly using the quizzes as part of the curriculum and not as an assessment piece, which lends more value to your instruction to begin with, I applaud that idea and hope others use this strategy as well!