Did a some checking for you. Looks as if you may very well have Stachys floridana which I just read goes by these common names:
Florida Betony
Florida Hedge Nettle
Rattlesnake Weed (there are several other weeds sharing this common name)
Here's the PlantFiles entry for it-
http://davesgarden.com/guides/pf/go/32086/
As you can see, there is only one photo of this plant and it is of the plant in bloom. Your photos are very good. If you believe I am right and you do have Stachys floridana, please take a moment to add all of your photos because it's real hard for people to go by a bloom when attempting to identify a plant and you have photos that people will relate to.
I've not had to deal with this weed myself personally but I've had to deal with hedgenettles. They're tough.
Now mind you, I've not had to get rid of the plant I think you have but based on a lot of poking around I did for you I think you might have to consider using a product that contains dichlobenil at some point in time. I only know of two, Barrier and Casoron. Of the two, I've only used Casoron before on Horsetail weeds. I got rid of the horsetails... and everything else in the vicinity using that product. Haven't touched it since.
Here's some information on dichlobenil-
http://www.wsdot.wa.gov/Maintenance/pdf/dichlobenil.pdf
Here's another article I found that looks very interesting that discusses the use of glyphosate to control Florida Hedgenettle. Glyphosate is the active ingredient in RoundUp-
http://pubs.caes.uga.edu/caespubs/pubs/PDF/C867-11.pdf
Please don't shoot the messenger but I don't think you should be trying to dig that up any longer. I think it's just going to laugh at you and come back to haunt you when it starts active growth this coming spring. Consider buying a few cheap stamp licker bottles from some office supply store. The kind with the sponge applicator tip like old style shoe polish bottles. They only cost about a buck a piece. Now fill it with RoundUp at regular strength not a concentrate. Sit down and bond with your Betony by sponging the undersides of several leaves on each plant on a day when your weather report states you will have air temps of above 60° for the next week. It is very important to wait for good air temps otherwise the plant will go dormant and you'll just be wasting your time and money on chemicals. Wait 10 days and re-apply. Don't dig them up when they start looking as if they are dying. Patience. Give the RoundUp a chance to work its way to the very tippy tips of all the roots and dig them up about a month later. RoundUp doesn't work overnight and generally you don't see signs that it is working for at least a week if not longer. If the RoundUp doesn't work, and I think it will if you apply it properly and at the right times, then try the Casoron which is going to be a lot more expensive and a lot harder to get your hands on.
Benefits of using a stamp licker bottle is that you're applying it directly to the plant you want to nuke so no risk of overspray or dripping on desirable plants.
Please post back how it goes with what ever route you decide to take. Stachys floridana is formally identified as being invasive and there will be others out there who are probably going to struggle with it. Best wishes to you.
