When my 2:39 time slot came up search found four hotels in the block that could hold my three attendees.  I selected each hotel, but alas, "We couldn't find any results for your search" each time I selected a hotel.  No hotel for me.

Alack, it looks like it was not just rooms to hold three people:

Sold Out Advisory!Due to enthusiastic turnout, the Gen Con 2024 attendee room block has sold out. Over the coming days and weeks we’ll be procuring supplemental inventory and making it available for booking on a first-come first served basis. If you were unable to obtain a hotel room on opening day or are looking to change your assigned hotel or room type, please check back periodically as inventory will become available through supply additions and booking cancellations. Thank you for your patience.

Gencon watched this happen last year.  Why didn't they reserve more rooms this year?

I realize "supplemental room block inventory will be made available for booking on a first-come first served basis" over the next few months and that I can try to get a hotel room every hour on the hour, but that stress and effort does not feel like a good experience to this seasoned enthusiastic attendee.

Where did you find that quote, not seeing it anywhere?  Inside the portal after you are allowed in (I still have 30 minutes)

Most reasonable hotels were sold out by 10:30 (pst) so we didn't even have a chance to book. 

My time slot was four hours after hotel reservations opened and, predictably, there was nothing left. I was looking for a room just for myself.

I then had a look at hotel rooms that are not part of the Gen Con block, but it turns out they are either too far (5.5+ miles) or crazily expensive (£600+ per night!).

So it looks like no Gen Con for me.

I'm genuinely happy for Gen Con that it's able to attract so many attendees, but deplore its planning. Clearly Indianapolis isn't a suitable venue since the city can't accommodate everyone who bought a badge. At the very least, Gen Con could have commissioned a shuttle bus company to ferry people between the convention centre and outlying hotels. That wouldn't have been ideal, but at least it would have been something.
 

https://www.wthr.com/article/news/local/groundbreaking-ceremony-held-on-project-that-will-reshape-the-indianapolis-skyline-pan-am-plaza/531-04e1bbb2-b0d7-44f4-9f00-0dc94e8d5832

Indy is connected by Amtrak.  Unfortunately, the 3 day a week schedule is extremely inconvenient for GenCon attendees (as in you can only do all 4 days by adding days on the front and back of the Con or miss some of it).  Also, a 10 hour drive (for me from the Philadelphia area) is a 21 hour train ride.  :(
 

Exactly my point. I took Amtrak to Gen Con one year from Cincinnati when I didn't have to be there until Thursday, but had to catch a ride home. It also shouldn't take around 4 hours to go the 113 miles between Indy and Cincy. If we had modern rail, it would be 30-45 minutes from Cincy, essentially a commute. I know all the reasons they won't do it, but just contrasting to the gentleman overseas how things are set up so differently.
I have lots of fun stories from coworkers who have relatives visit from overseas thinking they can day trip to NY or CA.

Indianapolis is the city with the most connected hotel space to a convention center in the entire country if I recall correctly, so if 5 miles is too far to go from your hotel there is likely nowhere in the country or world that could support Gen-Con.

My catchphrase is that the only wrong choice is not going, so I encourage anyone thinking being 5 miles away is a death sentence to hear that I was 12 miles away in 2003 and still had an amazing time (even being in a 5-hour-long badge purchase line from the infamous virus shutdown) 

Dallas also has airport trams direct from the convention.

I like Indy. But there are other options where twice as many rooms are available within walking distance.

The issue with Dallas is everyone has to Fly there unless you live in Texas. Indianapolis is within a 6 hours drive of a huge percentage of the US population.

Off topic people.

If you want to start yet another "Move Gen Con" you can do that with a new topic.

Mike