I am trying to work out if it is feasible to travel directly from Hong Kong to Dongguan.

Of course, it is feasible.
In HK Hung Hom Station, there are direct trains available to DG, the travel time is about 70 mins.
There are also direct buses available, at Metropark Hotel Causeway Bay, CTS offices in Prince Edward, Sheung Wan and Central area, you can take the bus.

From DG to Shenzhen, there are bullet trains available. The travel time is about 45 mins.
From Shenzhen, you can take the subway +MTR, or take a ferry back to HK.