Welcome to the forum!
I'm upgrading my front brakes now and learned a lot from this site:
https://www.cardomain.com/ride/2247236/1963-austin-healey-3000/page-2
3000 disc brakes used a Girling Type 14 caliper which has a 3.25" spacing between mounting bolt holes. The BJ8 (I believe from chassis no 26705) switched to a Girling Type 16 caliper with a 3.50" spacing between the mounting lugs. The BJ8 also switched to a thicker brake rotor.
Moss offers a ready to install big brake upgrade for the BJ8:
https://www.mossmotors.com/Shop/ViewProducts.aspx?PlateIndexID=96439
I don't know who manufactures the parts for the Moss kit and from where they are sourced.
Both Wilwood and Outlaw manufacture four piston calipers that will replace the Girling Type 16 caliper with the 3.5" spacing. Outlaw also manufactures a M16 caliper with 3.25" spacing for the earlier cars.
There is a good article on using Toyota 4 pot calipers to replace the G16 caliper here on Triumphs here:
https://www.vtr.org/maintain/brake-conversion.shtml I don't know if anyone has tried it on a BJ8 and whether it would work.
In the first article I cited it mentions using Mercury Capri calipers from early 70s cars as a cheap replacement for the pre BJ8 caliper. Unfortunately, the supply of right side Capri calipers has dried up and they are pretty much unavailable, so that option is kind of difficult.
I also looked into the cross drilled and slotted discs made by Disc Brakes Australia and sold by Moss:
https://www.mossmotors.com/Shop/ViewProducts.aspx?PlateIndexID=34603 Cross drilled holes have been cited as a source of cracking of the rotors and from what I could research, DBA manufactures its rotors in China. I went with these EBC rotors that are made in the UK:
https://brakespros.com/c-62_austinhealey_brake-rotors.aspx