I think that you could keep nearly all routing except ground on the component side and have an uninterrupted ground-plane underneath.
Its always worth spending time on placement and routing retries. It is educational.
Can CR2016 batteries supply the motor current required?
These batteries have about 80 ohms of internal resistance when fresh.
Stack up 3 of them and that's 240 ohms!
CR2016_Data_sheet_e.pdf (641.64 kB - downloaded 2 times.)
Worse still, this battery can only mange 5-15mA even under pulsed conditions.
Vcc could sag causing erratic behaviour in the attiny and the drivers.
Driver bulk caps could be made larger to help mitigate this, but its not guaranteed to work.
Route driver power Vcc and digital Vcc separately and only join them together at the power entry point.
Spikes from the driver/ motor could find their way into the attiny digital IO's causing more erratic behaviour.
The driver IC has internal freewheel diodes but I'd still add external diodes. They're a lot cheaper to replace than the IC. eg BAS40BRW.
A little advice. You need to work on creating more easily readable schematics.
Its very time consuming for others to unravel spaghetti.
Layout from left to right. Inputs on the left, outputs on the right.
There is no need to wire all grounds and power supplies together.
Make use of Global Labels (global signals) in the schematic.
A side note. Why not drive analog meters with PWM from the attiny? They typically only need 50 microamps for full scale.
You could remove the meter movements from their cases to repurpose them.