Hacking Rules Cyclopedia Surprise Rolls

The two d6s rolled for surprise can be consolidated into other pre-combat rolls. If you let the players roll one of them (knowing your side is surprised doesn't really change anything) they can be very versatile.

Almost all encounters should begin with a Surprise Roll to establish Party/Monster awareness. Surprise needs to be established first, because all other rolls are dependent on determining the state of awareness (Encounter Distance, Reaction Rolls, Attack Rolls, and so on).

Establishing Surprise can make combat a much riskier prospect (even for high-level play, a round of Monster Actions without preparation can be deadly) and ignoring or hand-waving the potential for Surprise rounds can potentially downplay player actions and decisions.

Other uses for the result of Surprise Rolls

It's Side-Based Initiative 
Surprise already determines “who gets to act first” in situations when one side is surprised. In the event of “neither side is surprised” or “both sides are surprised” re-purpose the dice as the initial Initiative Roll. Or if you don't like ties, on Even sums the players act first after Surprise is resolved, if the sum of the Surprise dice is Odd, monsters act first. The 2d6 bell curve makes 7s more common, so Monsters will typically act first. Maybe do Odd = Monsters in Dungeons (home turf advantage), and Odd = Players in a more level playing field.

It's Encounter Distance 
Encounter Distance is probably the most frequently ad libbed, overlooked, or hand-waved determination in older D&D. Since it is often directly constrained by the map in a Dungeon Environment, many DMs ignore random determination of Encounter Distance for planned encounters, or only use it for Wandering Monsters. The table look up required probably contributes to their disuse.

Encounter Distance is important because it directly influences the Combat Options available to the parties (Missile and Spell Ranges, Movement required to Engage in Melee, Weapon length, etc). Tactical decisions are player choices that shouldn't be minimized by fiat. It could also be said that the need to establish Encounter Distance before Reaction Rolls is important, as some forms of communication may be more challenging or impossible over longer distances.

Conveniently, Base Encounter Distance (Indoors/Dungeon in Dim light) is 2d6 x 10'. Use the 2d6 that were rolled for Surprise. Change the feet to yards outdoors. Halve product for No Light, halve it for Surprise, double for Very Good Light. While the ranges produced by this method don't match the Rules Cyclopedia exactly, they are close and much quicker than performing a table look up. Lower Bound is 10' (for Surprise in No Light), Upper Bound is 240' (Very Good Light, No Surprise, just barely in the longest Missile Range on the standard equipment list, the Heavy Crossbow). 

It's the Reaction Roll 
Blasphemy! But consider that a low sum of the Surprise 2d6 are probably surprise situations, which are not necessarily conducive to diplomacy, as the surprised party often reacts physically. In non-surprise situations the Surprise dice would be discarded anyway, so use them for the reaction roll.

If you re-roll Side-based initiative with 2d6 every round, consider folding this into the 2d6 Morale roll. This way Initiative is only redetermined when the tide of battle changes (the triggers for Morale Checks work well to reflect a change in the battlefield). 

Initiative

Determining the order of actions in an abstract combat system seems to be the topic du jour. Here's yet another idea to throw on the pile.

In most situations, use the To-Hit Roll to determine the order of action resolution. In melee, d20 rolls are being generated by each attacking character every round. Why not have them perform this double-duty and save the need for an additional roll. The need to establish “who-goes-first” might not be necessary until action is actually being taken in this case. As a T&T fan, my preference is to keep my combat abstract and quick, and I am used to determining how things are resolved after rolls have been made for the round. It could be easier to obtain the order of events when all the actions are out there (only instead of ordering things by declaration and having to deal with the "I changed my mind" or "But the guy I wanted to hit is dead" issues, this relies on a random factor).

This still might work better with Declaration-based, Phasic Combat situations. Since Spell Use does not necessarily result in a d20 roll, maybe Spells could be automatically assigned a number based on level/complexity, maybe they are just a modifiable (see below) "1" or "10" or just resolved last, to offer an opportunity for interruption (something I've always liked but found difficult to implement consistently). My gut feeling is that Ranged weapons don't necessarily need to have iterative resolution, but in any case you might want to refrain from resolving damage until the end of the round when using a system like this (another technique for embracing the abstract).

Here are some options/elaborations:

Use the Unmodified d20 roll to Determine Order of Resolution

You could go lowest to highest one round, and then highest to lowest the next to keep things random. Or if the first d20 roll is even, resolves High to Low. If it's odd, Low to High resolution. For side-based initiative, have Evens/Odds serve as a stand-in to determine if the Players or Monsters resolve first. There won't be ties this way.

Use the Final Modified Attack Roll

This will lead to higher level/HD individuals having their actions resolved first consistently, and could effectively makes any Strength Ability Score bonus a bonus to initiative as well, but this option could reflect experience, expertise and potentially even size (for large HD creatures) getting the first swing in more often. This seems pretty deadly (the Dragon's attacks are resolved first each round, meaning the parties actions are primarily reactive), maybe useful for a gritty/grim style of gaming. 

Modify the roll by Something Else

Modify it by Dexterity bonus or apply an Intelligence or Wisdom modifier (this might be sub-optimal for monsters, as their statistic blocks usually don't incorporate ability scores). Apply a bonus for longer/faster weapons versus shorter/slower weapons. Give certain Classes/Monster Types a bonus (one-time or level/HD based). Modify the roll for heavy encumbrance. armor type worn, or Movement Rate. Using modifiers like these might keep the order a little more randomized, and the best hitters will not necessarily be as likely to go first. I kind of like the idea of giving a bonus to Unarmored Swashbucker/Thief Types. Have a place for an individual's total Initiative Modifier on the Character Sheet.

Have the roll take place on a die drop sheet to track order-of-actions

I imagine a bulls-eye or race-course type situation, with rolls closer to the center/finish line going first. Probably pretty complicated without a constrained rolling surface (players love to throw those d20s).

Thoughts or glaring omissions/issues? Want me to work up some Examples? Again, these options heavily embrace the abstract nature of combat and wait for intention to become action before determining an order of resolution. The results will probably be pretty chaotic. I'll have to run this with my group a few different ways to kick the tires.