[RPG] ny way to gain additional reactions in a round

Travel Devotion is, by orders of magnitude, your best option

Losing some BAB, HP, perhaps skills, Skirmish damage, and Favored Enemy bonuses... are all worth it for what that single level of cleric can get you. Travel Devotion straight-up solves your movement problem, which not much else can say.

Pounce does not work

Charges specify melee attacks, so Pounce is useless to you. Swift Hunters can use Pounce, mind, but with melee attacks.

Greater Manyshot is deep down the feat tree, but works

Greater Manyshot makes each shot from Manyshot a real attack, letting you deal Skirmish damage on each one. Excellent solution, but at the cost of four feats.

Mounted Full Attack might work, but is very expensive

Some prestige classes give you the ability to make a full-attack while your mount moves. If you ignore the utterly stupid errata for Skirmish, which prevents using it based on mount movement, it could work.

Cavalier or halfling outrider (Complete Warrior), for instance. This route will take many feats and take a very long time (Cavalier requires four feats, most of which are useless to you, and gets it at 6th, while the halfling outrider requires two feats you might actually want, but doesn’t get it until 8th). Ashworm dragoon (Sandstorm) splits the difference with two feats, one kind of useless to you, and getting it at 7th, plus it gives you a decent mount.

Magic, psionics, mysteries

Hustle and dimension hop are low-level psionic powers that allow swift-action movement, knight’s move is a paladin spell that would work for you, and flicker is an amazing mystery that works kind of like Travel Devotion in that you set it up, and for next rounds/level you can teleport as an immediate action. All of these are limited and very difficult for you to acquire though.

Sparring Dummy of the Master

This thing requires that you either be a monk, or consistently hit very-high UMD checks. But, it turns your 5 ft. steps into 10 ft. steps, permanently. Very nice on any skirmisher.

Speed factor initiative CAN cut down on over-planning, without making play any slower, if you manage the tone and urgency well.

I have played a small number of times with it recently, after reading this article by the AngryGM (Warning: his material is written egotistically with much profanity). I liked it from a thematic perspective, as it would keep combat feeling rushed and uncertain. In practice, it accomplished that quite well. You engage all players at once for their main tactical decision, and then there is a much smaller amount of time per individual player turn. Thus, players are directly involved a larger amount of the play time.

There are some things to think about for this initiative system, though:

• Effects that last until the next turn can have wildly different efficiency. If you go high in initiative the first round and low the second, it is now a two round effect. If you go low first and high second, it barely exists at all. Possible houserule is to have the effect end on a particular initiative score.
• This CAN affect spellcasters more than it does martial characters. I had a Sorceror that chose to use Sleep, but the Axebeaks made it into melee before he finished casting. He chose to cast it at his feet rather than waste the spell. That could add cool flavor to your world (choosing the right spell for the job is tricky if you can't react fast enough to the situation at hand), but it could also frustrate your spell casters.

The last point is about your players. If they are very tactical about their combat, that may just be how they enjoy the game. Changing the flow of combat could be an exciting way to liven up the game for them, or it could destroy one of their central pieces of enjoyment from playing. I recommend trying it for a session or two, and then assessing if you will continue to use it.