OK, after a day of investigating and installing version 5.1 several times and copying 5.07 dlls to 5.1, I have found the problem.
The problem was in the OS2\dll directory.  It was one file.  The file is 
dspres.dll
The one found in version 5.1 is 455,064 bytes
The one found inversion 5.07 is 395,096 bytes
There were some updates made to DSPRES.DLL in 5.1, yes.
I wonder if I might ask you to try both of the attached versions of DSPRES.DLL and see if they exhibit the same problem or not.  (They both have a different subset of the additions made for 5.1.)
Hi Alex
I tried them both. They both create the same OpenChat trap as the original one included with 5.1. I switched back to the 5.08 version and OpenChat works just fine. So far, OpenChat is the only program that traps when using the new dlls.
11-14-2023  07:25:34  SYS3184  PID 0044  TID 0001  Slot 0070
E:\PROGRAMS\OPENCHAT\OPENCHAT-SMP.EXE
c000009b
000479c6
EAX=fffffff3  EBX=00000003  ECX=00000000  EDX=ffffffff
ESI=fffffff3  EDI=1b34e3f4  
DS=0053  DSACC=d0f3  DSLIM=5fffffff  
ES=0053  ESACC=d0f3  ESLIM=5fffffff  
FS=150b  FSACC=00f3  FSLIM=00000030
GS=0000  GSACC=****  GSLIM=********
CS:EIP=005b:000479c6  CSACC=d0df  CSLIM=5fffffff
SS:ESP=0053:000f86a8  SSACC=d0f3  SSLIM=5fffffff
EBP=000f8ffe  FLG=00010287
OPENCHAT-SMP.EXE 0003:000179c6
Attached is a picture of OpenChat when it works to give you an idea of the fonts used.