The way Kristen is preferring to do this is to use the onboard synth, in which case she should select either the GSWavetable synth (the oly viable option she listed) or the DXi/VSTi reroute option so she can use the Forte (which would be preferred here by far over GS wavetable synth)

Sounds like her physical connections are good. The realtec may have an update running in the background that keeps resetting itself as default synth, or windows may be doing it if she does not have the Delta selected as default windows device which she still has not confirmed.

Kristen,
you do not need the realtec to playback the GSwavetable synth or the Forte DXi synth as long as you have selected the M-Audio Delta 1010lt outputs 1&2 as the default outputs for windows.
You could select 'Monitor Mix' as well, but I use the 1&2 out here.
Confirm the Delta is selected as default windows device in Control Panel - Sound area.
Under the audio tab.

IF you do want your Yamaha sounds, you could easily hook up the audio outputs from the Yamaha to another set of inputs on the Delta 1010 - no need for the mixer manning1 spoke of, since the 1010lt has a fine mixer inside of it already.

The old drivers are stable, so if you liked them go ahead and use them as long as M-Audio says they work for whatever OS you are using. Is that dual core a 32 or 64 bit processor?

Make your sound your own!
.. I do not work here, but the benefits are still awesome