Okay, okay, it's not exactly the Beta Quest, but it's a way in.  We have found an Exit Modifier code that will conveniently place us in the Beta Quest (Beta Quest 000F, most likely).  All credits go to XDaniel, who discovered it on September 1st, 2002 (and my many apologies that it took so long!).  Here is the code and a list of tested exit values:
8016A717 ????

B=BETA MODE, N=NORMAL MODE, C=GAME CRASH
1000 = N/Intro
-1010 = B/Majors House
--1011 = N/Intro
--1012 = B/Southern Swamp
--1013 = B/Potion Shop
--1014 = B/Majors House
--1015 = C/Unhandled Opcode: Unknown
--1016 = C/Infinite Loop
--1017 = C/Infinite Loop
--1018 = B/Potion Shop
--1019 = B/Potion Shop
--101A = B/Potion Shop
--...
-1020 = N/Intro
-1030 = C/Unhandled Opcode: tge v0,v1
-1040 = N/Intro
-1050 = B/Majors House
-1060 = N/Intro
-1070 = C/Unhandled Opcode: tge v0,v1
-...
1100 = N/Intro
-1110 = B/Majors House
-...
...
            RANDOM CHOICES:
085A = B/Potion Shop
104F = C/Unhandled Opcode: sync
0313 = B/Potion Shop
491A = B/Potion Shop
F4F1 = C/Unhandled Opcode: tgeu v0,v1
0911 = B/Potion Shop
ABC5 = C/Unhandled Opcode: Unknown
21C2 = B/Southern Swamp
74BA = B/Bomb Shop
701D = B/Potion Shop
F4FF = C/Unhandled Opcode: dsra32 a0,v1,0x3

NOTE: It seems that only the second value determines active Beta Quest:
      7A = B/? Shop (Forgot Name)  -->> Exit to Great Bay Coast (finally a different outside area ;))
      BA = B/Bomb Shop  -->> Exit to Southern Swamp (activates Boat Cruise)
      88 = C/"WTF  Branch  NextInstruction=3"
      3A = N/Intro