JMeter slow with "Retrieve all embedded resources" - how do I scale?

Question

TLDR:

• JMeter crawls with just 1 test user if I select "Retrieve all embedded resources".
• JMeter throws Uncaught Exception java.lang.OutOfMemoryError: Java heap space in thread Thread if I test with 100 users
• How to eventually scale to test with thousands of users?

More details:

I'm recording the jmx script using the BlazeMeter Chrome extension. The user logs in, and completes a course and a test. There are many ajax requests being made along the way. Around 350 - 400 steps for the script. Mostly ajax POST request that have a json response.

When I click through manually in Chrome, the site loads quickly. Maybe a page load takes 2 seconds tops.

But when I import that script into JMeter with the "Retrieve all embedded resources" and "Parallel downloads" set to 6, and run it (in the GUI initially with just 1 user), it will get through, say, 7 steps quickly, and then just hang, sometimes for 10+ minutes before advancing to the next step. This doesn't happen if I uncheck "Retrieve all embedded resources", but I don't want to do that since that wouldn't be a realistic test.

If I take that same test and run it with 100 users (from the command line using JVM_ARGS='-Xms4096m -Xmx4096m' sh jmeter -n -t myfolder/mytest.jmx -l myfolder/testresults.jtl), I get Uncaught Exception java.lang.OutOfMemoryError: Java heap space in thread Thread and my computer fan goes nuts.

I have an HTTP Cache Manager configured with only "Use Cache-Control/Expires header when processing GET requests" checked and I've lowered the "Max Number of elements in cache down to 10 since that's the only way I can get the test running at all.

Ideally, I'd like to test thousands of users at once, but if I can't reliably get 100 users tested, I don't understand how I'm supposed to scale to thousands.

I see that there are other cloud-based testing options, and I've tried a few out now, however I always come to a halt when it comes to configuring how to test logged in users. Seems like most solutions don't support this.

Feels like the kind of thing that lots of people should have come across in the past, but I find almost no one having these issues. What's the right way to load test thousands of logged-in users on a web application?