Hi! Paul
You have simple rhythmic combinations disguised as complicated ones.
The first of each quintuplet comes on a main beat, so you should be able to practise this hand with confidence, emphasizing each main beat.
The other hand has three crotchets with two of them split into two quavers. Initially, leave out the second of each of the quavers and you should have no trouble playing this simplified bar rhythmically and with more and more confidence. Then insert the extra quavers and plough forward hands together!
Always think, and play, from the first beat of the bar to the first beat of the next bar - and do one bar at bar a time. Keep counting a very accurate first-beat impulse (but no metronome). You need the impetus of a high-jumper to land on the other side, ie. onto the first beat of the next musical bar. I do hope it works for you.
I think you should forget about the tapping. It makes it more complicated than it need be.
I am just about to contribute a paragraph in Piano Forum entitled “Three against Four - A Musical Solution", which you might find interesting. Good Luck. John