The website developer would need access to the server to build the website though, right? So that's my problem.
No. You could easily do that yourself, it can be made rather painless. Something like a dice site is perfectly suitable to run on heroku (or another platform as a service), and combined with a managed database -- it would be very possible to have the devs never touch the production environment.
Some things are definitely going to be harder without prod access (e.g. load testing) and maybe some weird prod bugs will come in, but in general it's very doable.
The issue you need to worry more about, is the code being backdoored not the production environment.
It's really annoying because even if I were to deal with a top company that has some of the best developers, they would charge me A LOT which I don't care too much about but the problem is there's no guarantee they wouldn't play with the seeds I just have their word.
If they don't have access to prod, they don't have access to the seeds -- and you'd rely on code review to prevent they're not leaked.
So the only options I have is to either learn how to code myself which will most likely take years or somehow find a developer that I can trust 100%. Am I right in saying these are my only options to move forward or is there possibly a way around the "not trusting your developer with the seeds"?
If you have lots of money, and want a gambling site built and want to put no trust in someone -- I can build it for you, seriously. I could use the cash, I just quit my job last Friday to focus full time on moneypot.com and had a few people wanted to leave also and work with me -- but I'm not making close to enough to pay anyone else's salary. To make it work, I'd need ~12k/USD/month with a promise of a minimum of 6 months -- which would buy you two full time devs (with bitcoin experience) and me managing it.
The way I'd do is is make the core gambling part publicly available (where public could be anywhere from open source, to downloadable to something you send to a 3rd party auditor) -- and I'd teach you how to manage the production environment, where you and you alone would have access and set the appropriate variables.