This is a typical process development issue for extrusion processes. One efficient approach is through nonlinear modelling. Several kinds of extrusion processes have been modelled with nonlinear modelling from a small series of experiments, and then it becomes easy to calculate the limits of line speed and quality variables, in presence of constraints on other variables, with a Lumet system. Two Swiss companies have good experience of this. Foam extrusion is more interesting because there are more degrees of freedom.
Well...never done foam, but have 20 years in plastic films.....I imagine you are running a flat die of some sort, an extruder, some sort of haul off device (puller).
My first suggestion is to quantify the variation you have in sheet thickness....is it predominantly in the machine direction, or in the transverse (across the sheet). I'm sure you have both, but you can separate them out by sampling at across the sheet at unifgorm intervals in length. cross web variations are usually related to poor mixing or temperature and pressure variations across the sheet. Linear variations can be caused by surging in the extruder (poor feeding of material), which would manifest itself as variations in die head pressure, or a cyclical variation that corresponds with a heater or coooling fan cycling on and off...most of these can be sorted by changing the temperature profile in the extruder.
The addition of a melt pump is a sure fire method of getting more consistant product and higher outputs.....
also preheating of the pellets prior to conveying lowers the internal shear and allows you to increase output.
You might also have some speed variation in your haul-off device (bad brushes in a motor can cause variation, as can slippage through a nip due to poor speed match between the downstream equipment)
Another thing to consider is die swell, die swell is related to the die gap and land length, it increases linearly with a decrease in land length, but it cubes with an increase in die gap...so if all else fails you can gain some improvemnet in output by increasing the land length (new die required...ouch)
Not knowing all the specifics of your process...I can only make generalizations.