Windows Server 2012 -- restore 75 day old file

Does anyone have an easy way then
the below to FIND the lost file since
I am willing to DROP "BackupExec 2012"
for a DAS, SAN, etc ?
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User calls saying they created a file
sometime on 6/3/14, saved it, waited
a few months, and cannot find it now,
stating that they might have MOVED it
to a different location or deleted
it in the last 75 days.

I currently have BackupExec 2012 and
lots of tapes which makes the process of
"finding all times a file has been modified
or deleted in the last 75 days" VERY slow.
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Steps, if using "incremental" BACKUPS
       ** restore 5/30/14 "FULL" end-of-month backup,
            see file is NOT there
       ** restore 6/02/14 "incremental" backup,
            see file is NOT there
       ** restore 6/03/14 "incremental" backup,
            see file is NOT there
       ** restore 6/04/14 "incremental" backup,
            see file is NOT there
       ** restore 6/05/14 "incremental" backup,
            see file is NOT there

       ** restore 6/06/14 "FULL" backup,
            see file is NOT there
       ** restore 6/09/14 "incremental" backup,
            see file is NOT there
       ** restore 6/10/14 "incremental" backup,
            see file is NOT there
       ** restore 6/11/14 "incremental" backup,
            see file is NOT there
       ** restore 6/12/14 "incremental" backup,
            see file is NOT there
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Steps, if using "differential" BACKUPS
       ** restore 5/30/14 "FULL" end-of-month backup,
            see file is NOT there
       ** restore 6/03/14 "differential" backup,
            see file is NOT there

       ** restore 6/06/14 "FULL" backup,
            see file is NOT there
       ** restore 6/12/14 "differential" backup,
            see file is NOT there