I leave to settle overnight before bottling and don't draw off the sediment. Just have a tank where the outlet isn't the very lowest point, just tilting your tank away from the bottom tap can do this OK.
If you press under ripe fruit or even just some varieties you can end up with a lot of starch that settles out overnight, this is best left behind too.
Plugs of gunk only appear in my juice if I draw off too much from the bottom of the tank. Sometimes I push my luck at getting a bit more out and it is always these last few bottles that have the gunk. You can as said shake it away and lay the bottles down. I have found that if you try to box up these bottles before they are absolutely fully cooled it will come back and be left as a deposit on the neck of the bottle after it cools and reduces in volume. Just don't draw off the bottom and it isn't an issue also make sure your ascorbic acid dosing is accurate.
Not sure what your lumps are, fortunately I have no experience of that. I am wondering if you are heating the juice and then bottling it. Maybe that isn't up to scratch and something is growing due to insufficient pasteurising.