Other answers have made a good case for the common interpretation. I have always thought that the ideal should approximate two independent voices played by different people. That can be particularly difficult for a player of "amateur abilities," but I encourage you not to give up. I despaired of ever being able to achieve that, but with some practice (less than I had thought), I was able to do it, at least to my own satisfaction.
But the reason for this answer is to address this part of your question, about Beethoven's intentions:
Do we know what Beethoven intended?
If you look at the first surviving page of the manuscript, at the end of the third line of music, in the right hand, you will see the triplet written directly below the dotted rhythm, and the head of the second note of the dotted figure is placed distinctly after that of the last note of the triplet. This seems like very strong evidence that the dotted rhythm should not be assimilated to the triplet.
There's a case to be made that this layout is not significant, especially if you see how quarter notes and half notes are not generally aligned with the first note of the corresponding triplet figure, but in the other place where the dotted figure appears in the upper staff with a written-out triplet (as opposed to the slash abbreviation), on page 5, the spacing is the same.
On the other hand, when the figure appears in the bass, at the end of the movement, the 16th notes do appear to be aligned with the third triplet notes. In two of the four cases, though, the triplet is on the other staff, with a bit of crossing out and correcting/editing in one of those spots. In the two cases where the triplet is on the lower staff, the stems and beams are colliding with one another, so everything is a bit crowded, and the alignment might have suffered because of that. I would be inclined to conclude that the alignment on the last page is less likely to reflect Beethoven's intentions.