I suggest you try using a SaaS product like this one I found online called RSVPify.

imo their pricing is super reasonable and the product looks great. It may be worth experimenting with a few options, this is just the first one I found that looked decent.

I spent some time experimenting with a wordpress event plugin but it wasn't really any good. It's possible that a 3rd party solution won't be a great fit, but this one looks promising - they even have copy catering specifically to non-profits.

If you end up liking it, the "EVENTS" button will link to your RSVPify page just like the "Donate" and "Merch" buttons do.