Maybe try keeping as much line as possible out of the water, eg by positioning the rod pointing skywards (but maybe not full-on "beachcaster mode"). If that doesnt work try casting a little further downstream so that any drag on the line in the water will be less able to move the lead towards the middle of the river. A final option is to use a thinner mainline - less resistance to flow. Some may use braid instead of monofilament.
If lead is still not holding bottom then you will almost certainly need to increase weight to hold bottom. In deeper moving water this may be unavoidable. Ideally you want just enough weight to hold bottom, that way a take can dislodge the lead and help to self hook the fish and /or give better drop back bites too.
Consistent rhythmic movements of the tip can be caused by underwater currents or swells and you need to ignore those as "background noise". Some realistic looking bites can be caused by leaves catching the line - so aim to keep line out of their path if they are following a set course down a line in the river.
Lots of tiny knocks can be caused by nuisance small fish or signal crayfish intercepting bait. If you are reeling in bare hook or mashed up hookbait without a clear bite that could be cause.