Newbie (ignorant) tech question

[Lionel]

I do have a question though about the particular signal I was referring to
above. This signal emanates from a 74175 TTL chip, and drives a Darlington
transistor, which in turn permits voltage/current to a small relay solenoid.

If you buy a 5V input SPST solid-state relay with mains-rated
contacts, it'd probably work fine straight off the output of your
74175. If the 74175 doesn't have the drive capacity (unlikely) to
drive both the new switch & the existing Darlington pair (the symptoms
will be that the solenoid, motor, or both fail to turn on when they
should), you could easily use a coupleof gates from 7400 or 74LS00 to
buffer the output of the 74175.
Omron make lots of solid-state relays that'd be suitable for your
task. You haven't told us the current rating of the 28V motor, so
you'll need to look it up or measure it before selecting a relay, but
something like this should do the job:

<http://www.digikey.com/scripts/dksearch/dksus.dll?Detail?Ref=136089&Row=403494&Site=US>
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Technical/Catalog Information CC1585-ND
Standard Package 18
Category Relays
Family Solid State
Vendor Crydom Co.
Type Triac
Current-Output -
Voltage-Input 5 VDC
Switch Function SPST-NO
Mounting Through Hole
Load Current -
On-State Resistance -
Load Current @ Voltage 1.5A @ 280V AC
Lead Free Status Lead Free
RoHS Status RoHS Compliant
Other Names LC241R-ND
-----

What I would be doing is essentially splitting that signal to a SECOND,
identical Darlington permitting current to an identical relay solenoid.
Will that signal from the 74175 have enough "oomph" to drive the two
Darlingtons, whose part number is MPSU45? MPSU45 crosses to an ECG272,
according to my ECG cross reference book.

Unless you like flushing money down the toilet, don't replace a common
part like an MPSU45 with an ECG part unless you're very, very
desperate.