Don't do it!
Sell it to someone who wants a Classic and buy a Standard, that would be my advice.
These have regular P-90s, with the same mount as on my SG Junior. I can tell you that that mount does not work with the baseplates on the P-90s made by Bare Knuckle. You will need to convert the pickup mounting to the screw-into-wood type. I found that shims were not necessary, there is plenty of wood under the pickup. You need to add foam under here though. That is a relatively simple operation for a tech but it will leave those two height adjustment screw holes either side of your pickups empty. This is why pickguard companies that sell pickguards for the SG Classic offer the option of deleting those holes.
If you want to go to the trouble of converting those mounts over I would recommend a Nantucket set or possibly a Nantucket bridge with a Blue Note neck. The Supermassive will provide more gain but is EQ might be too bassy for you. Another alternative is a Nantucket neck with a Pig 90 bridge and just turn the volume down on the bridge when you want less juice
If you convert it to humbuckers you will need a new pickguard and possibly some routing. If it has a PCB you might find it easiest to install a new harness.
By the greeting I am guessing that you are an Aussie. If you are in Adelaide you could take your guitar to Pete Jenkins (Dr Guitar) in Happy Valley, he did the pickup mounting conversion to fit my Stockholm P-90 to the SG Junior.
On the pickup mounting and the changes I made to my Junior see the following thread
https://bareknucklepickups.co.uk/forum/index.php?topic=31557.0