Hi Mark,
I would describe this stone as sandstone, I have used a lot of topical and impregnating sealers on this type of stone. Personally I would use a impregnating sealer when working internally as they contain no smelly solvents and the lifespan is normally longer.
No reason why you cannot use mop method to apply, I would suggest doing a small test area 1st, making sure all sealer has soaked in after about 30-45 minutes, before sealing entire area.
Regards,
Nigel Blake