Hi Matt,
For the suite I'd use m/s for sure. I've been getting excellent results on cotton suites by spraying a small amount of m/s and using a microfibre cloth to remove dirt (I use white microfibre cloths so you can really see the dirt coming off).
Have a bucket of warm clean water to hand to rinse out cloth after a few rubs. Also spray cloth with m/s after each rinse.
Most of the time doesn't even need flushing with upholstery tool, better to give a few dry passes though to remove as much moisture as possible! I towel dry as well to leave as dry as possible. Then get the air mover on the case to really speed up the drying.
As for the axminster, thoroughly vacuum first and keep moisture to a minimum, most of the time granules or powder used with an agitation machine and vacuumed up after will work for a general clean. If carpet is more soiled I'd lightly mist with m/s, agitate and give a single wet pass followed up with several dry passes.
For soot I'd thoroughly vacuum in all directions (firstly as standard then use crevice/hand attachment on hand and knees) to remove all dry deposits. Ultra pac is good but as Chris R pointed out let dwell and extract with fibre and fabric rinse to neutralise, use a hand or stair tool for extra flushing!
Draught marks are the same, vacuum heavily then use ultra pac, let dwell and rinse with fibre and fabric rinse after agitation with hand brush.
Just remember not to over wet and dry off as quickly as possible!
Hope this helps.
All the best,
Jason.