Spitting through the intakes can be an indication of a lean fuel mixture.
Whether that's due to the MAF or another problem requires more diagnosis.
A lean mixture burns very slowly or doesn't burn completely. This can leave some fuel in the cylinder in either an unburnt or "still burning" state after the exhaust stroke. When the inlet valve opens this can ignite the recently-injected fuel in the intake manifold, or, failing that, on a wasted spark engine, the "wasted" ignition event which occurs near TDC on the exhaust stroke can re-ignite fuel that previously hadn't fully burnt. The effect is the same. It flashes back into the inlet manifold.
Popping in the exhaust can be caused by a lean mixture but also by air leaking into the exhaust system, causing the engine to run rich (due to a false signal from the lambda sensor). Unburnt fuel then combines with the air that's leaking in and burns in the exhaust.
The fact that upping the fuel pressure makes a difference makes me think it's running lean and has run out of fuel trim to adjust it (normally changing the fuel pressure wouldn't make any difference because the ECU would trim the fuel back again).
It would need a look at the live data from the ECU to diagnose further IMHO. Has the ECU stored any fault codes?
Kevin