A couple of years ago, I was asked to be the registration chair for a national event, which we successfully held this spring. All previous events had been run strictly on paper-and-pencil mail-in forms, but that involves a lot of manual work, including a lot of last minute work at the event door. I looked long and hard at various open source and commercial event management offerings, and I spoke to other people who ran similar events. Based on recommendations from other event organizers, I landed on regonline as a good blend of features and customizability, even though it was a bit expensive (though they offer a discount for a 501(c)(3) organization.) What it came down to for me was effort. I wouldn't have time to set up all the hosting needed, to install and configure the software, or to integrate with a payment gateway, and I got a lot of really valuable features from their system. I didn't want us to make our attendees suffer through hour-long lines at a registration booth. And I was able to provide instant reports to the conference chair, who used them to help run the event smoothly.
Something it sounds like you need to do here is figure out "who is the Registration Chair"? If it's you, your only question to the Event Chair should be "what is my budget?" Base your solution on the bottom line. If your budget is $5/registrant, and it includes lanyards and ID cards, your options are wide open. If your budget is $0.50/registrant, and you have to use a box of old "Hello my name is..." stickers, your options are a bit more limited. The important thing is: the Registration Chair is in charge of registration. He or she decides how to best solve the problem, not "here are some random developers, you must write us a site."
One thing that still isn't clear is why you would have to "write" a new site. It sounds like you created one a few years ago, and then another, and then another. I realize your group is a precious snowflake, completely unique in the world, but events really are just events. They all have web sites, registrants, admins, venues, agenda items, merchandise, travel, lodging, taxes, payments, receipts, badges, volunteers, and reports. And there is nothing in that list you can't get from the marketplace. Ultimately, if you absolutely can't use a packaged solution because of [illogical rationale], you should only need to have someone reconfigure the existing site. That's a lot less effort, perhaps not much more than c/2014/2015/g
Finally, if you're taking payments on line, you're going to run into extra effort and risk to interface with them. No matter what, you really, really don't want to be responsible for someone else's credit cards. Not these days. The risk is more than you can imagine. If that's something you can foist off on a third party, you'll keep a ton of liability out of your organization.