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I know that the high atmospheric pressure on these planets make a unique challenge to learn about the planets interiors. Are there any active projects designed to learn more about the interior of the gas giants?

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The Juno probe will be doing some of this for Jupiter's atmosphere. Due to the extreme densities involved it will be doing so from orbit; not by entering into it.

From Wikipedia

Scientific objectives Image of Jupiter aurora in UV by the Hubble Space Telescope. Bright streaks and dots are caused by magnetic flux tubes connecting Jupiter to its largest moons (Io: bright streak on the far left; Ganymede: bright dot below center; Europa: dot on the right).

The Juno spacecraft's suite of science instruments will:

  • Determine the ratio of oxygen to hydrogen, effectively measuring the abundance of water in Jupiter, which will help distinguish among prevailing theories linking the gas giant's formation to the Solar System.
  • Obtain a better estimate of Jupiter's core mass, which will also help distinguish among prevailing theories linking the gas giant's formation to the Solar System.
  • Precisely map Jupiter's gravity to assess the distribution of mass in Jupiter's interior, including properties of the planet's structure and dynamics.
  • Precisely map Jupiter's magnetic field to assess the origin and structure of the field and how deep in Jupiter the magnetic field is created. This experiment also will help scientists understand the fundamental physics of dynamo theory.
  • Map the variation in atmospheric composition, temperature, structure, cloud opacity and dynamics to pressures far greater than 100 bars (10 MPa; 1450 pound/sq inch) at all latitudes.
  • Characterize and explore the three-dimensional structure of Jupiter's polar magnetosphere and its auroras.[17]

A recent analysis of data from the Voyager 2 flyby's of Uranus and Neptune found their weather layers were at most 1000km thick. I don't know if a followup to repeat the analysis for Jupiter and Saturn is planned or not.

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