Any hardware store should have them - they are the same ones used to sweep chimneys, just the attachments at the business end are different.
Do wear rubber gloves / gauntlets, overalls, goggles, mask
Do have hose / power-washer ready to use (BTW if you have a power-washer, you can buy a "silver-bullet" device that powered by the washer, worms its way through sewer-pipes, breaking up blockages)
I suppose its poosible for 3-ply paper to block drains, but if you are having on-going problems with the septic tank filling, you may have an issue with rain-water going to your septic-tank in the current weather.Do try pouring boiling water on a wad of toilet tissue in the toilet bowl. It should break up and flush away easily - if it doesnt, change your loo-paper.
Don't use harsh drain-cleaners / chemicals as there will kill off the munchers in your tank system
I think it is acceptable from a planning perspective to have rain-water from gutters / down-pipes go to a seperate soak-pit.
Any new water consuming devices in the house - extra showers, washing-machine, dish-washer?