The first idea makes perfect sense in theory. Maybe give it a test run? But you're wrong about the registration times being the same as the starting times. I checked 5 recent officials and only 1 fell into that category.
Maybe you're right about the lag, but it would need to be tested. I think the second registration will have dramatically less lag cause of 32 people missing it since they signed up for the first tourney. But any non randomized solution will have the same issue so that can't be helped.
I don't believe I'm being counterproductive when it comes to your second point though. In fact, if what you said about 2 registrations is your biggest con about it, then to me it makes the most sense to go with 2 registrations.
Okay let me see if I get this
What you said: 2 registrations are inconvenient because it forces a potential 32 people in a 64 person tourney to come back later and try again.
What I said: 2 registrations are convenient because it allows players to not inconvenience themselves by staying up late, waking up early, leaving class, getting on the internet at work, or ditching any other obligation to sign up for a tourney in it's 1 and only registration time.
You know what though? I'm speaking for the community with this suggestion and can always be wrong. Maybe people don't care about staying up or waking up early or leaving their commitments to sign up for a tourney that they're not guaranteed to get into. Maybe people who accidentally oversleep or had something to do or just forgot about it for 2 minutes don't care about getting a second chance.
I'll say this though. It's a global game where I met lots of cool people from Eurasia. I see a lot of people talk about how they didn't sleep til 4 am or 6 am because they wanted to sign up for a tourney. Along with myself, I've heard people say "oh well, guess I'll leave class for a bit to sign up for this tourney". I've heard people say "dam I can't believe I stayed up until 3 am to be 20th reserve" before. It honestly makes me slightly sad knowing that people do this because they enjoy the competitive gaming aspect of pokemmo and they're forced to sign up in these ways.
TL;DR
If you could allow people to have fun in this game without sacrificing sleep and obligations, why wouldn't you? Because you'd rather not have people be inconvenienced by failing to sign up at a time that was convenient for them and letting them have a second chance? Okay. If I didn't get through with this post I'll just give up trying.