My laptop has recently decided that 60 Mhz is enough of a refresh rate
and I beg to differ. My eyes are killing me.

I would like to set the refresh rate to 75 or higher while keeping the
resolution of 1400x1050. It's a t43 266884M running Windows XP.

When I Control Panel | Display | Settings | Advanced | Monitor it
shows Wide Viewing Angle & High Density RexView Display 1400x1050 as
the monitor. In the Screen refresh rate drop-down, only 60 is
available, even when I choose not to hide modes not available from my
monitor. When I change to a lower res, I can select higher refresh
rates at the lower resolutions, but they look suspiciously like 60Mhz.
I want it at 1400x1050 anyway. I have tried upgrading the drivers to
no avail. The

The IBM support line don't want to support me above 60 mHz, saying
that's the standard for Thinkpads. I swear I didn't used to have to
put up with this.

If you're talking about the LCD screen, then there is no "refresh"
rate as LCD pixels are either on or off all the time.
For an external display, you may be hitting the limit of the RAMDAC on
the integrated graphics chip.

You can try using a freeware tool from EnTech Taiwan
MultiRes which enables you to access and alter the display settings
available through the display driver.
http://www.entechtaiwan.com/util/multires.shtm
For making advanced custom settings you can use their PowerStrip which
is try-before-you-buy and reasonably priced.
http://www.entechtaiwan.com/util/ps.shtm

I installed that prog. Makes it quicker to change modes but doesn't
list any additional refresh rates.

power strip will sovlve this problem, but most LCD screens only support 60hz  ,
anyway, try it 
download it here
http://www.entechtaiwan.com/util/ps.shtm
have fun