[Mondial]

Brenda, its going to be real difficult to get the 6L6 to clip symmetrically. Typically, a single ended amp has a lot of second harmonic distortion because of the nonlinearity of the tube grid-plate characteristic. The tube gain is highest at high plate current and lowest in the region of cutoff, which is what you are seeing. So the amp always clips on the cutoff side first.

If you look at the distortion vs. power output graph of the link below, you can see the single ended distortion at 6.5 W output is about 10% and almost entirely second harmonic. This is the non-symmetrical clipping that you are seeing. The 6L6 is not really great as a single ended amp.

https://frank.pocnet.net/sheets/127/6/6L6G.pdf

That's precisely the reason the 6L6 is normally used in push-pull. In the P-P configuration, the second harmonic is cancelled out and the load can be optimized for minimum third harmonic, which becomes the major distortion component. Looking at the data, the THD at full output drops from 10% single ended to 2% in push-pull.

You may be able to get the amp to clip more symmetrically by playing with the bias and/or screen voltage. I just noticed that you mentioned that your screen voltage is higher than normal. This may contribute to the clipping if the grid bias is not adjusted accordingly. With higher screen voltage you may need more negative bias on the control grid to center the bias point in the middle of the tube input-output characteristic, making the output clipping more symmetrical.