I thought I posted this message in January but on browsing the site today I discovered I had not.
I have searched all the Ayrshire Old Parochial records for Hillas and other derivations of Hillhousebut might have missed Hilas one l spelling.
The only Births recorded for St Quivox are two entries for Frances Hillas born March 24th 1852 Reg/Dist: 612.1 /2 St Quivoxparents William Hillas and Margaret Downie Frame CH2V10 and Frame 502.
It may be that although your William was born in St Quivox the birth was recorded in the OPRs ofPaisley Abbey Renfrew.
If you have had no luck so far please let me know and I will look up the Pailsly records the next time I go into Glasgow. I fyou wishh to search all the OPRs yourself you can do so for a charge via the Scotlands people site.