Checked your post in feedback section, point 2) is just dialog box error from original D2, dont know if it was fixed by blizzard in later patches but for your information MedianXL is based on Patch 1.13c.
What you described in point 1) there, is also not a problem caused by mod, simple thing is that Horadric Scroll, Horadric Cube, Staff of the Kings and Amulet of the Viper isnt locked as linear, so you are free to get any of those pieces in order as you wish and NPC's dialogs can be triggered in different ways cuz of that. The only difference between original game and mod in that matter is that you got Horadric Cube from start cuz Halls of the Dead (where Cube originally was) is used as transition to Uber Levels. In short, same confusion you experienced in mod can be found in original game.
To confirm or deny your problems with The Summoner quest triggering out of nowhere I used my untwinked characters which im currently playing on hardcore, playing them all simultaneously with similar levels so was able to try two 'Entering Act2 scenarios".
What you said earlier "I noticed that you start the game with the Horadric Cube, presumably for crafting purposes, but this causes quest glitches in Act 2." is not true cuz it didnt cause anything wrong, will explain it further. When you starting Act2 in mod you got only opened Quest 2 which saying "Take the artifacts to Cain in Lut Gholein" and after talking to him its changed to "Search the Halls of the Dead under the Dry Hills for the Cube. Search the Maggot Lair under the Far Oasis for the Shaft. Search the Claw Viper Temple for the Headpiece.". For me all seems fine cuz you got already Cube and should continue with looking for Staff and Amulet. I did talked also with each NPC in Act2 and nothing unusual occured at this point, I also didnt left town thru gate yet. Next step was to go and get rid of Radament plus take Horadric Scroll, killed him but when opened chest then no Horadric Scroll droped from it, so explain to me how you droped Horadric scroll if you talked earlier with all NPC's , have you left town gate maybe before that? At this point no The Summoner quest was triggered.
What you said in initial post "also, the quest in my quest log allows me to play his dialogue that normally plays when returning the Horadric Scroll to him." is not true. Tried it in game on realm now and Cain is only speaking "You have quite a treasure there in that Horadric Cube. According to Horadric lore, the Cube can restore a Horadric Staff. To do it - use the Cube as you would a scroll. When the Cube opens, place both pieces of the Staff into it and use the Cube's transmute power. You'll be pleased to know that the Cube has other alchemical uses as well... Six gems plus one sword transmute into a socketed long sword. You may also transmute two quivers of crossbow bolts into one quiver of arrows, while two quivers of arrows yield one quiver of bolts. I must leave it to you to discover other formulae." which is as it should be. Due to Horadric Scroll not droping in first scenario, with second scenario I did not talked to Cain at all and had Scroll from chest and after that talked with Cain and he opened only above dialog.
For both scenarios after some time waiting near Palace, Jerhyn is like teleported near you with
! and he is triggering The Seven Tombs quest.
Now Im not quite sure that you did what you said in that thread, have you didnt mentioned some steps you made like leaving town, messing around or anything else? Cuz as I said earlier no The summoner quest was triggered with both scenarios I tried. Curious if you was able to recreate The Summoner problem in your other single player game.