Looking at the descriptions again, along with the early audio interview with Greenwood, the biggest problem with the HIBAL balloon explanation is Greenwood's assertion that the object 'jumped' around the sky quickly, in addition to occasionally appearing stationary or moving more slowly. Other aspects, such as the colour, size, shape, etc, could be reconciled with a balloon, as in this particular case could the arrival of military personnel afterwards. Keith Basterfield claimed to have identified a specific HIBAL launch that could be the culprit (flight 292) although most project records have been destroyed, and flight 292's entry was, frustratingly, missing from the logbook of the chase plane pilot!
http://stratocat.com.ar/bases/42e.htm
The subsequent apparent takeoff of the balloon / object was explained by Skeptoid - as usual, based on someone else's solution - as a separate sighting of a towed target drogue - which is again possible I suppose, although again it doesn't completely fit with even some contemporary descriptions of the original sighting.
Overall the balloon is a reasonable generic fit, with some issues in specific details. Again this seems to come down very much to whether you trust witness descriptions. In this case they are fairly consistent but one of my main concerns is that most of them, eg Greenwood, had been primed to look for something very unusual - in his case by someone running into the class and announcing a "flying saucer". From that point everyone would have been looking out for strange things.
As usual these days it's hard to search for information on this case due to search results being dominated by crappy podcasts, so here are a couple of links to actual ufologists debating the HIBAL solution:
Basterfield
Bill Chalker
Bill Chalker again