I have William Mallin's bible, and in it he names only the one wife, Elizabeth, so I don't think he was married before. As he was born in 1772, children born in the 1780s to anyone with the same name are probably not his. But it could complicate matters to know that there was another couple in the same parish with the same name.
I noticed that freereg.org says that they have transcribed the marriage registers for All Saints, West Bromwich starting in 1795, but I could not find any marriage for William and Elizabeth using their search engine. Freereg says that the register is in bad shape and hard to read, so I suppose that one of the illegible entries could be for William and Elizabeth. It's too bad to hear this about the register, because so much of my family was from that parish!
I have searched Tipton St Martin using freereg, the IGI, and the newer databases at familysearch.org and not found anything. In fact I searched those databases for someone named William Mallin marrying a woman named Elizabeth anywhere in England during the 1790s, and didn't find anything that looked reasonable.
I recently discovered that the All Saints WB register was never microfilmed by the Mormon church. They only copied the bishop's transcripts, which I've already checked. I still suspect that William and Elizabeth got married in All Saints, but if the register is illegible, I won't be able to prove it using that source. Do you happen to know whether the banns registers survive?
I do think the Christ Church burial record that you found is that for my ancestor, and I think you probably have the right burial records for his parents, too.
happy new year,
Dale