From my recollections from when I was imaging using a Sirius mount, a two minute exposure should have some some trailing caused by periodic error. Hypertuning can improve this but won't eliminate it. If you're running your mount using EQMOD from the computer, you could get an inexpensive eyepiece webcam that's compatible with PHD2 and use that to generate a PEC curve. EQMOD can add this curve into the computer's control signals to the mount using "pulse guide". The only restriction this adds to your using the mount is that you must always park the mount before powering it off to maintain the PEC synchronization with the gear train.
At some future time when you get a guide scope, you can use the webcam as a guide camera. Astro cameras that do this are the QHY5II and similar cameras. These are frequently called "solar system imagers". I've also guided using a previously retired Meade DSI I mono camera.
Polar alignment is critical for unguided imaging. You can drift align your mount using your camera by taking 70 second exposures at the standard drift alignment points. With the slew rate set to 1x sidereal, track for 5 seconds, slew E for 30 seconds then slew W for 35 seconds. If you're perfectly polar aligned, you'll see stars with a tail that passes back through the star. Polar misalignment shows up as a V shaped tail that misses the star. Adjust the polar alignment and repeat until you're satisfied with the alignment.