Dillon, Gillingham, Kramer...all worthy of consideration.
Dillon's an interesting case. He played for some very bad Packer teams (best record was 6-6 twice), out of the spotlight in Green Bay at the time. His career was relatively short, 8 years, though not unusual for the era. As noted below, a few Dillon DB HOF contemporaries with equally short careers are in the Hall. Those contemporaries might present a problem in themselves.
When Dillon retired 2nd. all time in INTs, the guy in first place was the legendary Emlen Tunnel, primarily a safety, who had 74 picks over 11 seasons by that time. The equally legendary Night Train Lane, albeit a CB, began his career in the same year as Dillon and by 1958 had 44 picks to Dillon's 52. Lane however suffered from what Dillon experienced in his final season (and what the best DBs experience today): opponents stopped throwing at him. And Lane kept playing and playing through 1965.
Other Dillon DB contemporaries in the Hall include Jack Butler (CB, 1951 - 1959), Jack Christiansen (S, 1951 - 1958) and Yale Lary (S, 1952-1953, 1956 - 1964), though Lary got points for being the greatest pre-modern punter.
So, 5 of the 24 DBs in the HOF had their prime years overlap Dillon's 8 year career. It's interesting that 3 of those 5 (Lane, Lary, Christiansen) played for Detroit in the 1951 - 1964 period, though Lane arrived in 1960. Christiansen and Lary both played on 3 Detroit championship teams. Lane came later, and did not play for a championship team at any point in his career.
Further, if we count Renfro and Lott as safties and Woodson as a CB, there are only 9 safeties in the HOF, 3 of which were in their prime during Dillon's career. Tunnel and Lane in particular cast a huge shadow, as does Christiansen's 3 rings (assuming they were handing out rings at the time).
Gillingham? Well, the voters are biased toward very long careers when it comes to O-Linemen. A disproportionate number of the modern HOF players posted more than Gillingham's 10 seasons (with one season lost to injury). The timing of Gillingham's career is something of a double-whammy. On the one hand, his first two seasons were the last of the Lombardi championship years so he suffers from the "how many Lombardi Packers are we gonna put in?" bias. On the other hand, his All Pro and Pro Bowl recognition didn't come until after the Lombardi years, so he suffers from the "bad team" bias.
Kramer? We know the drill...the "too many Lombardi Packers" argument and, of course, "Instant Replay".
Are any of these good reasons to exclude these players? Probably not.