I think there are some suggestions I can offer, but first I wanted to check with one of the comments that you have made.
You say that characters with a d6 in shooting can't hit. This seems a little off because the odds for hitting a TN of 4, i.e. a target at short range with no cover, are 75% for a Wild Card. I certainly have players in my games with d4s and d6s in shooting that have no problems with hitting, especially once you take into consideration how frequently a d4 will explode (1 in 4 chance).
Assuming that you are applying the rules properly, I can suggest a few things that will improve the situation:
Melee Combat
Ganging Up - This gives +1 to hit for every ally in combat with your foe up to +4. Even if a character isn't hitting they can assist with giving bonuses to other people.
Push Manoeuvre - This relies on the Strength Attribute rather than Fighting Skill, and allows you to move the target around, cause damage if you have a shield, or knock the target prone.
Wild Attacks - These give +2 to hit and +2 damage, and are extremely effective. Watch out for the reduced Parry you get though.
Smarts/Agility Tricks - These have a similar effect to Taunt and Intimidate, but are more dependent on good teamwork as the -2 Parry on a simple success only lasts until the affected creature's next turn.
I'd try and be as flexible as possible as GM when players come up with ideas for tricks. One of the best examples I've ever had is with someone who grabbed a can of baked beans and threw it whilst shouting 'grenade!' - as a successful smarts trick it had all of the enemy diving for cover
Ranged Combat
Aiming - Do nothing for a round whilst you aim and you get +2 to hit, which is very effective.
Using a shotgun (depending on the setting) - gives +2 to all shooting rolls if you fire a single barrel. Makes you more likely to hit an innocent bystander though.
You've also got double tap (+1 to hit and damage), and three round burst (+2 to hit and damage) with certain weapons.
Other general comments
There are a few general Edges that can assist with low skill combat characters. One that springs to mind is Elan, which gives +2 to any roll you make as a result of spending a Bennie.
Consider giving non-combat characters things to do whilst others are fighting. Dramatic tasks are good for this, but get a bit old if overused. For example, your computer hacker is trying to break into a security system so you can escape the room you're in whilst the rest of the group are holding back the drug enhanced super mutants.
Also don't forget that a successful trick, taunt or intimidate with a raise will shake your opponent, making them MUCH easier to wound. For high toughness creatures this becomes a hugely valuable tactic.
Also, there are a couple of general resources that you might find useful:
Savage Worlds Combat Survival Guide - which summarises the options you have, along with suggestions as to when each of these might be used. It should be noted though that there are a couple of new options introduced in the Deluxe version of the rules, e.g. pushes, that are not covered on this sheet.
Whispers From the Pit - Expanded Trickery - which goes into details about tricks and how to run them as GM. ... looks like this site has been corrupted
Best Answer
There are really only a few ways to speed up combat, and most of them really depend on what is bogging you down. Here is the advice I'd give if you really want to make sure you get through as fast as possible:
Limit Turn Time. This is the biggie, and you're already doing it with the carrot method (providing a chip worth a +1 to any d20 roll). That's great. I'd introduce a stick too, make them delay if they aren't ready to act. We've done this, and it works pretty well, though it can get a bit stressful if you have a character with a lot of options. This should fix player attentiveness too.
Create Flow Charts. Ask people to spend some time out of game mapping out their options. Sit down with your players (especially the ones who are regularly victims of analysis paralysis) and map out what powers and abilities they want to use in specific situations. Develop flow charts or rainbow tables if you have to. The should then be able to consult these during other peoples' turns to determine their optimal move and decide whether they want to do that or something else.
Plan Your Turns. Make sure your players are spending their time between turns planning out what they are planning to do on their turn. They have a good bit of downtime between turns, this should be spent mapping out their next turn (obviously some situations will come up that change this, but for the most part, you should know what you're doing by the time your next turn comes around). If you have your options well mapped out, this should be even easier.
Identify Party Synergies. Especially in paragon tier where your players are heading, it's fairly easy to develop a party wide strategy (whether that's radiant mafia, murder pinball, frost cheese, or any other common party wide strategies), that will not only make your party more effective, but will lead you to faster combats as you can more easily wipe out enemies.
Use Essentials Characters. Most essentials characters have fewer powers and options, the majority of them have things that fire when they make a basic attack. This is a great thing for new players, and players who regularly suffer from analysis paralysis. Fewer options means faster play.
Roll Attack and Damage Dice Together. If the attack hits, great, total the damage, if it doesn't ignore the damage roll. A subset of this is to have your dice read when you take your turn.
Use Average Damage The next step is to do away with damage dice all together. Use the average of the dice that would be rolled (d6 is 3.5, d8 is 4.5 etc). If it comes out a fraction, round up or down, your choice.
Use L1 Equivalent Damage. This is something our DM and I are discussing to speed up our Paragon tier combats. They are too slow right now (an average, relatively easy combat takes 2+ hours, and a complicated one can take 4 hours or longer). We would up monster damage and reduce their HP so that the fights are quicker, but deadlier. They would consume about the same amount of party resources (the point of most fights), but they would last less time.
Speed up DM Time. It sounds like you're not having trouble with monster turns (that's one of the big time wasters in our games), but average damage, or rolling damage with the hit roll can save some time. As can simplifying the monsters down to just a power or two instead of the several that monsters often have at higher levels.
Simplify Out of Turn Actions. Starting in Paragon and moreso in epic, out of turn actions become a huge time drain. They are great for getting more attacks, dealing more damage etc, but they can be a bear to resolve. Talk to your players about how to resolve this (many characters, like even midlevel battleminds have a lot of them and are reliant on them for effective play). This could include choosing character who don't use as many of them, or some other way of simplifying them (Don't remove them entirely, opportunity and immediate actions are important resource pools, and removing them will make entire roles(Defender) obsolete.
Rejigger Initiative. Have all the monsters go, then all the PCs go. This is a bit more common for PbP games than live play ones, but it can help speed up play.
Ultimately though, I'd talk to your group, do they enjoy hour long easy combats or are they annoyed by them too? Do they have ideas on how to speed them up?
You've got a great resource at your table for figuring out how to solve this problem. Your players. Talk to them (out of session, or before) as a group, and perhaps as individuals and try to figure out a solution that works for your table. No one thing is right for everyone and it may take some further experimentation to find the right thing. Identify specific things that take time (is there a lot of our of character chatter, does play stall with a couple of players all the time), and try to get to the root of it.
That said, 4e's combat mechanics, while well laid out and very well balanced are not constructed for rapid play. They are designed so that the majority of each session will be consumed by combat and that each combat will take a good amount of time. If I'm remembering right, they expect and average Heroic tier combat to take an hour. I've rarely had a normal heroic tier combat take less than 2. So manage your expectations here, you're probably about where most groups are.