I've looked up another gaming site but no games matching your description so far.
cd.textfiles.com has a DOS shareware game called
Plunder, with the following description:
Quote:
Plunder 1.0 (Herringbone Software; $6) you
must use your skills as an archaeologist to
uncover ancient ruins from Scotland to Iraq.
As you dig trenches and pits in your search
for long lost treasure, you must watch your
budget. You can either get rich quick or go
bankrupt just as quickly.
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It's an ASCII game though, and doesn't seem to feature time travel too.
Also, while not much of a help, I found a selection of
archaeology related games at the Museum of London website.