Is Udemy the best place for a webinar for game devs, or should I look elsewhere?

If you're bootstrapping, pay yourself less and re-invest in the company. If you've raised money, then pay yourself average salary as you aren't subsidizing and getting more stock (for the $$) as an investor would - so once you raised, then it's a shared risk - don't make the financial subsidy a thing you take on. I see this happen so many times where venture funded founders pay themselves little (ex: $40K / year) to look good, but the truth is you should be making $75K and instead you don't have the financial resources to a) pay off personal debt, b) hire help to be able to have more time to work, c) enjoy life with your partner/family and in turn burn those relationships. Don't make that mistake if you have financial partners as investors. Be fair, but don't take a financial loss every month to save face.

Have you considered utilizing a tool like Webinar Jam? You can pre-record your webinars, turn them into evergreen webinars and set the entire system up to provide specific dates and times for the recording, including a, "Your in luck, our next one starts in 15 minutes!" option or something like it. Three weeks is a long time to wait when we are a society that want instant gratification so offering something like this may be a key for more frequency. Also, if you have a way to monitor the open rate of those five reminders, I'd encourage you to look at that statistic. Even though your current schedule is three weeks out, five reminders seem a little high and I'm thinking you'll see that the two out of the five e-mails don't even get looked at. Other suggestions would be to look closely at your webinar title, the length of the webinar and even the hook you are pitching to encourage people to watch. You want to give off a high perceived value to entice registration and attendance.

GoToWebinar all the way. It's a bit pricey (but not too much), but it's by far the best solution out there. The last thing you want to do is use a free/cheap but unreliable provider and have your webinar experience massive connectivity issues or drop half way through.

Marketing & Sales. A lot of entrepreneurs are "doers of the thing" but at some point, you're forced to take the shift and become a "marketer of the thing". Think of it this way: You can have the best product on the market, but it doesn't matter if noone knows about it. Ofcourse, there are so many other important bits I'd love to tell you about - but, start with these and you will see traction, the rest will follow.

Everything you do (in life and as an entrepreneur) should start with an underlying passion. If you aren't pursuing the things you're most passionate about, you're doing it wrong (or just for the wrong reasons). IMHO. So in that regard, I'd highly recommend reading Simon Sinek's "Start With Why". If you're not up to reading a book, just Google his TED talk as a start.