Long Exposure SiriusXM Satellites

I've taken pictures of satellites before and even created a video of SiriusXM satellites going into Earth's shadow, but I thought doing a long exposure of the satellites could look really interesting. In my head I'm imagining two little dots of the satellites surrounded by a field of dramatic star trails. One of my problems is I don't own a remote shutter so when I do multiple 30 second exposures there is usually a gap in the star trail between images, especially noticeable at the high zoom needed for photographing satellites. Also touching the camera could knock things off slightly and images wouldn't be as nicely aligned, so that's not preferable.

I took ten minutes of images and was really underwhelmed by the result.

Both satellites are clearly visible, but there are very few star streaks. Also the gaps in the streaks is painfully obvious and distracting.

I'll have to find a solution to the remote shutter and try for a longer set of pictures to gather more star trails.