Registering people on mobile at an event – form field best practices

I’m working on a mixer event where we hope to get people registered for our community. We have a lot of young people so working on doing an text-to-register option. They text a code, and get a link to a registration form in mobile browser.

The problem is our old registration form (paper) has a number of fields (maybe 20--contact data plus other information), but having that many fields in a registration form isn’t that user friendly for mobile, right? Conundrum: we want to make registration accessible on mobile, but would really like all that data. I know things like form pre-population and drop downs are better for users, we're a small org and don't have a lot of form customization options. Plus some of the fields would require massive configuration for things like a dropdown (like researching/typing in hundreds of options).

Should we just make like 4 fields mandatory and the rest optional? Or should we just have 4 fields, then we can follow up with an email to get more info later? Another option I'm not seeing.