Can a participial construction modify an adjective?

It was a very dark, cloudy night, and they were a bit late arriving at Hagrid's hut because they'd had to wait for Peeves to get out of their way in the entrance hall, where he'd been playing tennis against the wall. (Harry Potter)

In the example, a participial construction seems to modify an adjective, late. Can a participial construction have the same function as a to-infinitive does, or does this have the role of something else?

Why is that any different from the following?

I was late getting to work this morning.

We thought we got away without being seen, but were soon getting our comeuppance from Mrs. Ainsworth.

I was crazy thinking I could pull the wool over their eyes.

All of these are normal, grammatical constructions. And so is Rowland's passage, even though it does run on.

It seems to me that the adjective late is modifying arriving. They were arriving, and they were late when doing so.

That said, a participle can indeed modify an adjective.

The cheering yellow colour of daffodil buds promised an end to dreary February.