Couple things with that TOCC. While that station may be closer, it also requires 10-20k people to walk across Newmarket Rd and then through residential streets. They already shut down a lane of traffic on Roma St for pedestrians, I don't think Newmarket Rd or Granville St traffic could handle that? The station isn't a hub and will require multiple trains for people on the East, South and West. The Bowen Hills station has from what I can see 3 or 4 separate lines operating through it. So most people will be able to catch 1 train and end up there. Abbortsford Rd has three lanes of traffic each way, so it can handle one lane being close for pedestrians. There is also an entertainment precinct within walking distance from Perry Park which is serviced by multiple buses and ferry's.
But these are exactly the things that would also be upgraded. With regards to the 750m and 1.8km both are correct in their own ways. If you go from (the newly refurbished IIRC) Wilson Station down Vardon Street (or Murray Street) to the end it's about 500/550ish meters and mostly down hill (so we can probably round it down for actual walking). If we were then to then walk across the open and largely unused Finsbury Park, MJ airwalk jump across the Breakfast Creek, and walk to the center of the field we are totaling just a hair under 800 meters but as I pointed out before most of that is down hill so I think calling it 800m total even if you are going to the far side of the stadium isn't unfair. Moreover there is also Murray Street that is a tiny bit shorter but isn't as much a main street. (I'll try to attach a screenshot of the area and where I imagine a bridge might go, if it will work for me!)
I would also point out Lang Park is a much more mixed (up and down) 1km. Whole Perry Park is only 600m from Bowen Hills Train Station however the Ferry is a 1.6km from Perry Park so I think this is largely irrelevant. I think discussion about the Busses is largely irrelevant the addition or changing of bus routes is in my opinion is like squabbling over the cost of changing the locks when buying a house, the cost here is largely irrelevant and with a redevelopment the increased use would result in more services being provided. I would also add that 'Game Day' Busses' are quite normal particalry for the GABBA (and leave from Carindale, Chermside and other similar hubs) and I imagine trains but I've never noticed.
One can assume any revitalisation of Ballymore would include some kind of upgrade to the bridges/walkways as well as Finsbury Park. Comparing Ballymore and Perry Park the key differences really lay in the surrounding space and parklands and lack thereof in the case of Perry Park. Ballymore is roughly 125,000 m^2. It has a quite nice function center, and is surrounded by parklands and such on the other side of the Breakfast Creek (totallying around 100,000 m^2); moreover Ballymore is in a fairly low density residential area (particularly when compared to Perry Park). This can be contrasted with Perry Park that is in a largely industrial/commercial area. Perry Park only offers less than 50,000 m^2, and little in the way of other facilities that could be retained / repurposed.
The last thing is that Ballymore is literally a financial drain and is very decrepit. This is painfully obvious when you consider there have been at least 3 nearly actioned plans to upgrade Ballymore, Howard was going to do it in 2008 because it was desperate for it then, it's been a decade since. From what I have seen of Perry Park it's fairly modern and isn't as desperately in need of an upgrade.
Also one other thing that no one has really brought up (that I have seen) is that the RNA showgrounds could also be considered an option. But I think it fails on all the most criteria... except needing a revitalisation.