I think we might need to clarify point 4. If you fight in the PvP match, you get xp that can be beneficial during the mission (leveling up). Killing players and their henchmen is also an interaction, even if it's your henchmen that do the killing. Which steps can a player take to avoid interactions during a PvP match?

Pre-searing ~100% quest speed-run

Rules

1. All quests should be done, unless explicitly mentioned otherwise. a) All Vanguard quests are excluded. b) Adventure with an Ally is excluded because it relies on another player. c) The Prize Winning Hogs and The bear hunters are not a "traditional" quests, i.e. they do not show up in the quest log, and are therefore excluded. d) Quests that require a different primary profession are excluded. e) When locking in a secondary profession, some quests will become unavailable. The quests that were doable[1] before locking in a secondary, and would become unavailable after, must be done before locking in the secondary. Failure to complete these quests results in an incomplete run. The quests[2] that would be unlocked if another secondary were chosen are excluded.
2. Timer starts when character is created and the first load screen is done, and stops when the load screen for post-searing Ascalon shows. a) Both /age and seconds are required. b) Time waiting for access to Ascalon Academy, and possible time spent in the PvP battle, will be deducted after the run is completed.
3. No event consumables are allowed.
4. No interaction with other players/accounts are allowed. a) No trading. b) No adding another character to a party, or joining a party.
5. (Additional category) No /bonus items are allowed, e.g. no fire imp.

[1]: These are NOT excluded: The Elementalist Experiment, A Mesmer's Burden, A Monk's Mission, The Necromancer's Novice, The Ranger's Companion, and Grawl Invasion.

[2] These are excluded IF you chose a primary/secondary combination which results in you not having the required profession:

1. Elementalist a) The Supremacy of Air
2. Mesmer a) Domination Magic
3. Monk a) Protection Prayers b) The Blessings of Balthazar
4. Necromancer a) The Accursed Path b) The Power of Blood
5. Ranger a) A Test of Marksmanship b) Unnatural Growths
6. Warrior a) The Vineyard Problem b) Warrior's Challenge

Pre-searing Any% speed-run

Rules

Same as the ~100% quest category above, with the exception of rule 1, i.e. no quests are required. Get to post-searing as fast as possible.