This will be a bit of a jumble of thoughts, but wanted to provide my experience with this bike.
I own the bike you're looking at purchasing in addition to their Smart.Shift Gemini - I mostly bought it since it had been upgraded by the first owner with a lot of parts I was looking to buy separately. I did use the Apollo last year on a 600k permanent in northern New England (hello from NE Randonneurs) and a handful of populaires. I wrote a ride report for that
here, where you can see some pictures of the bike along with some notes throughout.
You will find many, many impressions of the Alfine 11 system online. Some people have lots of issues, some don't (i.e. this 63-page
forum topic, this
shorter reddit thread). Shimano may have updated the Alfine 11 since the forum topic was created in 2012, so maybe take some of those with a grain of salt.
Your satisfaction with the Alfine 11 system will depend tremendously on the terrain and grades you plan to ride. If the only limitation was the ~400% gear range, you could either just be really strong when it comes to climbing and accommodate the reduced gearing that way, or you could shift the gear ratios of the whole system via the ratio of the front and rear belt cogs and accept that you won't be able to push as hard on the flats/downhills.
The issue with either approach is that the Alfine 11 system's max torque specifications are quite low if you are going to climb or really crank. Some folks have pushed the envelope by using gear ratios that go beyond the specified range of 50 N-m input torque - some have noted it's okay, some have said they've toasted multiple hubs.
I opted to ride it with the standard gearing and 650b x 48c tires that the prior owner outfitted it with. Going up anything more than a 10% grade was a decent struggle, especially on that 600k through the White Mountains. The hub did slip with a "clunk" a few times when under heavy load, which has me worried about its longevity/durability. The system is HIGHLY sensitive to cable tension, so make sure to learn how to tune that thing beforehand if you get it. Riding it for long durations without the tension set properly will absolutely toast it. The system will often let you shift under load, but you must not give into the temptation to do so or you will eventually destroy it.
I'm pretty sure the brifters that come with the dropbar model (my understanding is they now offer a flatbar version) are rebranded Microshifts. They get the job done, but they aren't anything spectacular. In particular, I'm not in love with the shape of the hoods compared to Shimano/SRAM.
When it comes to belts, I both love and hate them. Functionally, I love the reduced upkeep they (generally) require - I can just hose the bike down after a ride. But with the muddy and gravelly conditions I typically ride in, I've had serious belt squeak issues that drives me nuts. Spraying it with water quiets it down for 5-6 miles, but then it'll resume again. It sounds
like this (from my Gemini bike). Some folks online have mentioned that my belt is likely spent, but it's only got something like 5k miles on it. Based on other folks getting much improved mileage, either there was something wrong with this particular belt or they aren't as resilient to gravel/mud conditions as I would like.
Based on my experience, I think either a non-electric Rohloff or Pinion system is the best (non-conventional) bet for randonneuring applications. I haven't used a Rohloff myself, but I have used and owned electric and mechanical Pinion bikes. The electric pinion system for dropbar bikes is fine if you're willing to make some modifications (I had so many issues with the TRP Hywire levers that I ripped them out and threw on some
modded Shimano Di2 levers). You can read a lot about my thoughts in my 1-year review of the
Priority Smart.Shift Gemini here. In the
TL;DR, you'll see that if I were to do it over again, I would've bought a used Priority 600 on the cheap and modified it with after-market mechanical dropbar shifters instead. That said, if you're fine with flatbars, the standard gripshift is excellent.
Hope that helps!
Andrew