Alasdair,
What you describe sounds like ‘loll’. The boat will float but leans either side or the other which is a stability issue.
Brief description here:
https://www.wartsila.com/encyclopedia/term/angle-of-loll
Paddlers like yours with their shallow slim hulls are particularly susceptible to this which is why I chose Bilsdale for my prototype with it’s much fuller ‘chunkier’ hull.
From my experience with Bilsdale, there are two main factors with the model. Firstly the paddles need to be properly immersed and the plans should show the waterline to be aimed at to achieve this.
Secondly, the ballast must be as low as possible to achieve maximum stability. Sometimes this is not possible within the shallow hull so alternative measures are needed. Even with Bilsdale’s high displacement hull I found there was an issue and the solution was to add ballast to the bottom of the hull. This can be done by adding a weighted false keel or simply by attaching ballast to the bottom of the hull where nobody will notice it. I went for the latter solution using self adhesive motorcycle wheel balance weights with a waterproof resin coating. See photo below.
You can run a test on this by suspending a steel or iron rod/bar immediately beneath the keel to see if this improves stability,
When I motorised my Revell Queen Mary 2 Kit I had exactly the same problem and the boat needed a substantial external keel to keep it stable whilst maintaining the designed waterline. See other photo.
Colin