The in tank fuel pump has a filter on its intake, so surely that cannot had sucked up 'crap'? Unless it fell off?

Plus, with all the cornering a car does, and on low fuel, everything is going to get sloshed around, so thinking that all the 'crap' sits at the bottom waiting to get sucked up into the fuel system is not the case surely?

I think the low fuel and jolting the next day is just coincidental and your problem is ignition related, either coil pack wiring, spark plugs or HT leads.