Approaching this from the technical side instead of the legal side (I am not a lawyer either, but let's see if we can come up with a lightweight solution that can prevent anyone from needing to be a lawyer).
First, as has been noted here, don't associate these domains with your personal GoDaddy account. The account portion of the registration is completely free, so there's no reason not to set one up and dedicate it purely to the domains for the company/project. This is good practice in general, and protects against all kinds of scenarios that may come up even if you are very good at dodging buses. Domain registration is more painless than you might think, you can do all of this in well under a day with essentially no risk of downtime or other disruption.
Here's the key element: assign the account to a mailing list, not an individual user's email. When registrations go through, they will go to the list, not just to you. If someone needs to reset the password to the account (e.g. if you unexpectedly win the lottery, move to Tahiti, and blow all this off) they send the password reset link to the mailing list. Anyone can do it, but if they do then everyone will see them doing it. Assuming you guys are all more or less friends and the scope of the project isn't too broad (obviously don't do this on a mailing list/project with open registration) this should be roughly the right amount of overhead for this process.
If it's a huge project with people in mission critical leadership positions who you don't feel you can entirely trust, then unfortunately it's probably time to get some legal recognition of that if , and the domain registrations are only a tiny part of the reason for that. I'm also assuming that GoDaddy does not make your entire credit card info readily available (I haven't been a customer there for some time) if this is not the case then clearly this isn't an ideal solution.