When will the next transits of Mercury and Venus occur during a total solar eclipse?

The last transits of Venus occurred on June 8, 2004 and  June 5, 2012, with the next pair predicted for December 10, 2117 and December 8, 2125. Transits of Mercury are much more common, with the most recent one occurring on May 9, 2016 and the next one on November 11, 2019. It is not unreasonable to ask when we might expect such transits to occur during the time of a  total solar eclipse. The next anticipated simultaneous occurrence of a solar eclipse and a transit of Mercury will be on July 5, 6757, and a solar eclipse and a transit of Venus is expected on April 5, 15232.