Scott, look up the parameters for MSCDEX. It has been too freaking long since I used it and do not have DOS help available. What you want to do is make sure that the CD mounts as H: all of the time (and they may also be a function of the CD driver in config.sys - I have not had a DOS disk or CD for about 5 years). I would actually make X: or Z: really.
Next, in autoexec.bat, Z:\i386\winnt.exe as the last.
Do check out Bart's PE online (google it). You can boot PE, diskpart the C: to prep it (delete, create, and format partitions), copy i386 to C:, and then run winnt32 from C: for an even faster install. Because PE runs as 32bit with full memory usage, the install is much faster than the 16bit DOS install.