The report list is controls by a list defined in the application config file. In the install folder (usually C:\Program Files\Trimble\Trimble Business Center), there is a file named TrimbleBusinessCenter.exe.config. This file holds the application configuration that is normally not modified by the user. If you edit this file, (it's just an XML file) you can change the number of reports displayed in the report pull-down list and the default reports. The part of the file you need to edit looks like this.
<ReportMenu>
<!--Number of items-->
<add key="Length" value="10" />
<!--Defines the order of reports in the report menu.
The reports defined in this section will be the first reports in the report menu.
The order is the order they appear here. Reports not defined here will be placed after
the defined reports in alphabetical order.-->
<add key="Baseline Processing Report" value="5c0759ef-637a-43d9-b2f0-7e4475356fb1"></add>
<add key="Earthwork Report" value="8d864779-280c-4785-b475-ea6ab071ebd9"></add>
<add key="Import Report" value="FB55F2CC-8546-4112-8397-5ADF88005FCC"></add>
<add key="Level Report" value="a0750924-5ff1-4267-b326-37554b6a604d"></add>
<add key="Network Adjustment Report" value="2e88f88f-23de-4865-a117-f1a272dedc31"></add>
<add key="Point Comparison Report" value="EE3A121D-2A75-4EA0-852E-97E2061EAFE6"></add>
<add key="Point Derivation Report" value="a43d5f8e-7c32-4ead-b100-7e38cfc09468"></add>
<add key="Point List" value="9460b6dd-768f-47e4-9e14-b5d31000c582"></add>
<add key="Project Computation Report" value="5D2FD8BD-3D44-4192-BDED-1DDA6973F0BD"></add>
<add key="Site Calibration Report" value="12c1a592-e810-4564-83af-588b2f9806d5"></add>
</ReportMenu>
Since the default is set to show 10 reports and 10 reports are pre-defined in this config file, there are no open "slots" for other reports. That's why changing the "Show on reports menu" property did not make any difference.
It sounds like you just want to delete most of the pre-assigned reports and maybe increase the number of reports to display in list. (change the "10" to something like "15")
So this section of the file would look like this;
<ReportMenu>
<!--Number of items-->
<add key="Length" value="15" />
<!--Defines the order of reports in the report menu.
The reports defined in this section will be the first reports in the report menu.
The order is the order they appear here. Reports not defined here will be placed after
the defined reports in alphabetical order.-->
<add key="Earthwork Report" value="8d864779-280c-4785-b475-ea6ab071ebd9"></add>
<add key="Import Report" value="FB55F2CC-8546-4112-8397-5ADF88005FCC"></add>
<add key="Point List" value="9460b6dd-768f-47e4-9e14-b5d31000c582"></add>
</ReportMenu>
This would add the three reports to menu and then the first 12 reports found in the report options list with the property "Show on reports menu" set to "Yes".
If you are going to edit this file, please make a backup copy as if you mess up, TBC will likely not run at all.
To edit a file located under the C:\Program Files folder, you need to move/copy the file to a location where you have edit permission (like your desktop). Then edit the file and finally move/copy the file back to C:\Program Files\Trimble\Trimble Business Center.
Good luck....