The big question is, when do you start timing it and when do you stop? For MESSENGER (you mention you're most interested in James V. McAdams' work on its trajectory analysis, for which he was named the 2008 Engineer of the Year by the AIAA Baltimore Section), McAdams himself starts one of the related publications (MESSENGER MERCURY ORBIT TRAJECTORY DESIGN, AAS 03-209, PDF) as:
After nearly three decades of Mercury orbiter spacecraft mission
studies, recent improvements in ballistic trajectory design and
spacecraft technology opened the door to low-cost mission options.
And later in the same document:
During the last 15 years, space agencies around the world have
invested heavily in studies of “comprehensive” Mercury orbiter
missions that often require advanced propulsion, two orbiting
spacecraft, and sometimes a lander or surface penetrator.
So as you can see, it's tough to precisely pinpoint when MESSENGER trajectory analysis started. So I would suggest looking for when mission specific information was made available, to enable further refinement of its final trajectory. I would suggest the date of publishing the 1998 Discovery Program Announcement of Opportunity (AO), which (quoting IMPROVEMENTS IN TRAJECTORY OPTIMIZATION FOR MESSENGER: THE FIRST MERCURY ORBITER MISSION, AAS 01-458, PDF):
... imposed restrictions on launch dates, available launch vehicles,
and total mission cost. Thermal protection, propellant mass fraction,
and a comprehensive science payload left one choice – the Delta
2925H-9.5 (formerly 7925H-9.5), which is the highest-performance
expendable launch vehicle allowed within Discovery. The Delta
2925H-9.5 launches from Cape Canaveral Air Force Station, thereby
limiting declination of launch asymptote (DLA) to ± 28.5˚ without
performance degradation. The AO guideline that “a mission launch
every 12 to 24 months,” the AO requirement “that launch can take place
by September 30, 2004,” and a Discovery mission (CONTOUR) launch set
for July 1, 2002, all constrain any MESSENGER baseline and backup
launch opportunities to begin and end between July 1, 2003, and
September 30, 2004.
Announcement of Opportunity: Discovery Program, NASA AO 98-OSS-04, was published on March 31, 1998.
So now all you have to do is decide when to stop considering any work being done on MESSENGER's initial trajectory analysis. Perhaps its launch date on August 3, 2004? Or maybe its first Mercury flyby in January 2008? Depends on how much of its trajectory would you like to include in this timing of yours, but MESSENGER is currently still on its extended mission since March 17, 2012. And its trajectory is still being designed and periodically corrected. Your call.
For also a pretty interesting read, here's Takuto Ishimatsu's thesis for Master of Science in Aeronautics and Astronautics at Massachusetts Institute of Technology: Interplanetary trajectory analysis for 2020-2040 Mars missions including Venus flyby opportunities (35.61 Mb PDF). And if you're interested in more convoluted trajectories, I'd suggest looking at the work on the ICE/ISEE-3 one. It's simply fantastic, but it's still being worked on too, 36 years after its launch. I currently don't have a good link for it's trajectory design available, but it shouldn't be too difficult to find with a web search, it's been all over the news recently.