Break the Hall of Fame down to periods of time. The best (pick a number) players from each period:
1876-1900: The Pioneers
1901-1910: Deadball
1911-1919: The Early Days of Prosperity through World War I and "The Scandal"
1920-1932: The Golden Days of Baseball
1933-1946: Through the Depression and World War II
1947-1960: Integration and the Age of Television
1961-1968: Expansion and a Period of Transition
1969-1981: Further expansion, the Designated Hitter and a Work Stoppage
1982-1993: Rabbit Ball and parity
1994-2004: The Age of Many Questions and Few Answers
2005-2013: Present Day
Also you would have sections that pertain to
(a) The Negro Leagues
(b) Foreign Baseball
(c) The Dominican Influx
This would alleviate the PED issue. Go ahead and induct the ones who have the numbers (i.e., Bonds, Clemens, McGwire, etc.) - just the fact that they'll be in the "1994-2004" Group will indicate that they "possibly" played under suspicion. Maybe they did, maybe they didn't...who knows?
Or you could break it down this way:
1876-1950: The "Whiskey" Era
1951-1975: The "Greenies" Era
1976-1993: The "Cocaine" Era
1994-2013: The "PED" Era