Or, you could put manuka honey on the injury and provide the glucose directly where the healing energy is needed, along with the antibacterial properties of the honey. Manuka honey is being mused medically to treat long-term diabetic ulcers and bedsores and the published results in the medical journals are very promising.

Yes, carbs can definitely help wound healing. Glycoproteins need glucose, so a shortage would likely impair their formation. Also, car ohydrates are protein sparing because protein doesn't need to go towards gluconeogenesis. Lastly carbohydrates help recycle vitamin c, a deficiency of which, as you noted, will slow wound healing. Many paleo sources of carbs contain vitamin c too.

Vitamin D and skin repair This study shows correcting vitamin D deficiency improves skin healthing.

However this study used 50,000iu vitamin D each week which is not the most sensible way of restoring vitamin D status. How much vitamin D you require depends on how fat/skinny you are so using 1000iu/daily vitamin D3 for each 25lbs you weigh adjusts intake to body size. Up to 10,000iu is safe for daily use to raise 25(OH)D quickly. After 3~5 months a 25(OH)D (vitamin D) test will enable you to see if that daily intake is sufficient. If not increase by 1000iu/daily for every 10ng/ml under 50ng/ml or reduce intake by 1000iu/d for each 10ng/ml over 60ng/ml.

You may also want to consider improving omega 3 status.

This study Fish oil supplementation alters levels of lipid mediators of inflammation in microenvironment of acute human wounds used 1.6 g of EPA and 1.2 g of DHA per day (You need to look at the EPA and DHA numbers rather than used just 3 g fish oil daily. I find it's quicker/easier to use a concentrated liquid fish oil that provides EPA 650 mg DHA 450 mg per teaspoon so 3 teaspoons daily more than covers it)
They conclude that fish oil is likely to be cost effective in improving wound healing. They also suggest that people with poor wound healing may have suboptimal intakes of suboptimal caloric intake and lower than recommended daily intake of protein, vitamin C, and zinc. So it may be worth checking those as well.

I've definitely experienced this as well as I mentioned in my question Sport and Starches. I play a fair bit of ice hockey and while on full paleo with minimal starches or even limited starches (post-hockey) I noticed that bruises on my legs were taking FOREVER to heal. I haven't kept the actual data for it so I suppose it's not very scientific, but experience tells me that now that I've upped starches considerably healing time is AT LEAST twice as fast.

I've also experienced much better recovery from some HIIT sessions I do. Once a week I do lactic acid tolerance training with massive resistance of 30sec on / 1min off about eight times and it destroys my legs as you would expect. Before I sometimes had to put off the next session (aerobic training) days later just because my legs weren't close to ready. Since adding in starches however, I've seen improvements that are borderline astonishing. Keep in mind I'm eating loads of starches in most meals, but now I feel ready to go the next day if I have to and no longer have any hesitation about whether I am fully recovered.

As to why this happens? I don't know, and maybe somebody with a good background in Biology could help, but it seems to me that since every cell in the body uses glucose that only by providing it in ample amounts will you operate at full efficiency. I'm sure on a cellular level recovery and wound healing would be a pretty taxing event. Sure, if you're not taking in glucose your body can go through processes to convert it but as in all cases of conversion it won't be optimal and you'll probably be running on fumes. So your cells take what they can get and make due but there's a bottleneck in the process and they are running at low efficiency. Add the starches in and give them all the fuel they could ask for and BOOM, Wolverine healing.

I have noticed increased speed of wound healing on Paleo. But I eat some carbs everyday (of which partly starchy), I think about 100 gr. I also keep my omega 3 intake above the omega 6 intake and take opti-men multivitamin 2 per day.