A couple of ideas:
1. Different shorts with thicker pad.
2. Two pairs of shorts.
3. If you have any old shorts with padding, cut it out & sew on top of pad in another pair.
4. Sew in a layer or two of carpet padding.
5. Different saddle.

I suspect thicker padding won't help, but is easy to try. I find thick padding bunches up and tends to have an effect opposite of desired.

I had problems a couple of years ago with bruising the twins. I have been using an ISM Adamo Road saddle (no nose) with good results. It isn't very comfortable for longer rides, but serves the intended purpose well. Not sure if it would help you, but it got me back on the bike.

Good luck.