There aren't a huge number of published pictures of BG from that or any other time, prior to his being arrested. It seems like a bit of a reach to say it couldn't have been him because he wouldn't have been dressed smartly.
In the images from his interrogation, before he was put into a forensic suit, BG was wearing a smart white shirt with no tie and the top button undone--very similar to descriptions by some witnesses. He can clearly make himself look very smart when he wants to. If he was stalking a particular target (such as Jill) he may very well have wanted to look good.
I also wouldn't consider going back to his flat to put a jacket on to be "get(ting) changed." Jill herself was wearing a long coat. It was only around 12C outside that morning and it appears there was light rain:
weatherspark.com
I don't think the scenario is improbable at all: that he would go out early, loiter around for a few hours, pop back home to put on a jacket, go back out, kill Jill, rush home to change into a completely different outfit, and then try to form an alibi for himself.
We also don't know that he "go(t) back to Gowan Avenue just in time to catch Jill arriving home." We have no idea how long the killer (BG or otherwise) might have been there.