Hi Tom
I had a look earlier at this and really struggled to find more children than the two you mention
You have the main facts I am sure including death of Basil Snr in 1797, there is an entry on Scotlands People for that year in the Wills & Testament section.
I also found the possible first marriage of Harriet and a divorce a couple of years later, 1791 and 1793.
With the marriage in 1767 and the death by 1797, you would think there would be some reporting of the Alves children by Basil and Elizabeth. Basil Jnr.'s death refers to him being the youngest son. I can't see anything though, sorry - hopefully someone else can add more for you

Monica