I’m running Ubuntu on my machine currently and logs are flooded with
psmouse serio1: Wheel Mouse at isa0060/serio1/input0 lost synchronization, throwing 2 bytes away.
and my touchpad stops working briefly.
I’ve seen other reports of a similar issue on other distros and a recommendation to compile the driver for PureOS into the Kernel.
I’m not sure how I would go about trying that, or if there is another solution that i am missing.
Would someone be able to break it down for me, please?
Well, it seems we have a touchpad unsupported by the community : Input: psmouse - disable automatic probing of BYD touchpads
There is even indication that we will never have two-finger scroll capabilities. 
Sad for a so-called open hardware.
I wonder if I can try to change the controller.
Otoh, it looks like we can still activate BYD detection with the following :
echo -n "byd" > /sys/bus/serio/devices/serio1/drvctl
You need to understand that BYD touchpad is NOT open hardware, our devs are doing their best to write a driver without any documentation whatsoever. I am sorry, you’ll need to rely on such hack (that is: if you are not using PureOS).
As Mladen pointed out, the touchpad needs to be reverse engineered (and this takes time and skills, because the part supplier provided absolutely no documentation for it). For what it’s worth, I’ve seen it working out of the box on Fedora 24 and Fedora 25 (and it seems to behave better in F25)… BUT… a recent kernel version (4.8.13+) broke it completely. I filed a bug about that in the Red Hat bugzilla for Fedora, but obviously that’s something that you must report either in each distro (because they vary in package versions and thus behavior) or upstream directly with the Linux kernel bugzilla.
Actually, the basics features of the touchpad work out of the box in Debian Stretch (so no multi-touch but right side scroll, lower side horizontal scroll, 1,2,3 fingers click).