I think I see where you guys are coming from in terms of combat speed but I think you missed some important elements. The concept of combat speed is basically the same as action points from other games such as X-COM. The difference though is that the various actions you can take in that game have different costs whereas yours all cost 1 (or maybe all for spells/attacks eventually). Here are a few ideas I think you could make to improve things.
All the numbers are just off the top of my head so please don't place to much weight on the particulars. Just look at the overall consept.
1) Keep the term combat speed but once you get to tactical combat convert those to action points. Give the unit 5 action points per combat speed (or try a few numbers and see what number works best). So a unit with 1 combat speed now has 5 actions points, a unit with 2 combat speed now has 10 action points. The reason for this is mainly to give some flexibility without introducing lots of decimals. There are other options that accomplish the same thing but this is the one I am basing the rest on.
2) Because of #1 it should now cost 5 action points to move over plains. A bit more for forests, hills, etc.
3) So far things are basically the same just with different numbers and names. The first real change would be that each weapon (or any item you use) should be given an action point cost instead of a combat speed modifier. Why? Well carrying a halberd should mean you attack slowly but shouldn't mean that you necessarily all of a sudden can't move. Doing this gives lots of flexibility for interesting weapons that have real differences and removes the current problem of tieing movement and number of attacks together. Now you have the halberd that takes 5 actions points to swing and you have a dagger that take 2 actions points to swing. Dagger attacks twice, halberd attacks once for a normal unit but they both still move 1 square a turn.
4) Armor should be handled differently as well. Instead of giving a combat speed modifier it would have a movement point modifier. Let's say you have a hero now with 2 combat speed which gives him 10 action points. We have researched some type of very heavy armor (full plate or whatever). This armor could modify how many action points it takes to move. Let's say it gives a movement penalty of 2. Now it costs the unit 7 points to move 1 square. He still moves 1 square a turn but if he stands still he could attack multiple times. If he is wielding a fast weapon he could even move and attack in the same turn.
5) Mounts - basically the opposite of what was described in #4, they would give a movement bonus and don't effect combat speed at all. As above but now it maybe costs 3 or 4 points to move a single square (or maybe percentages would work better). Unit is faster but can't attack more frequently.
So to make things simple you do the following. All equipment now has 2 potentially new stats in addtion to what you already had. If it's an item you use such as a weapon or a potion it has a cost to use. All equipment also has a movement modifier and still has it's combat speed modfier. Combat speed should be thought of as hasting or slowing the unit. It will move faster, attack faster, do everything faster (or slower), consequently it should rarely be used. Movement modifier effects just movement. Wearing or wielding something extremely heavy then it slows you down, riding a horse or wearing boots of speed and you move faster.
I know you won't implement this, especially at this late date but I really feel the current system is limiting. The idea behind it is good but in my opinion it wasn't utilized correctly. You are basically using an action point system like is commonly used is squad based tactical games but have tried to simplify actions to a single all-encompassing number. I see you trying to make changes to compensate for this but no matter what you do movement and attacking will be tied together or you will make a compensation that will severly limit things (i.e. can't move after attacking, having attacking use all action points, etc). After release I think you guys should really sit down with some games that use action points and try to come up with a system that works more like they do or at least offers the same flexibility. I'm sure some will mod some kinds of changes along these lines in but I really think the base game should have them.