I am assuming you are using column based kit. You can heat the extraction buffer to 60 C and then add on to membrane, let it sit for 3-5 min and then spin it.
After applying the elution buffer to the column, you can centrifuge first at very low speed (around 50 g). This should ensure that the elution buffer reaches every part of the membrane. After that, you follow by applying the high speed centrifugation as usual.
That DNA is pretty big...the kit purification methods unfortunately cause major shearing problems with DNA larger than 5kb. Can you skip the purification on column and Ethanol ppt. your product? Sometimes the old fashioned way is best. When isolating genomic DNA, I still resort to gentle rocking in Ice cold ethanol and then fish the strands out with a disposable loope.
If you are planning to use SpeedVac (I use it quite often with good results) remember to use low adhesion microcentrifuge tube. That should increase your final yield.
We use a standard Qiagen kit to isolate and purify human genomic DNA from buccal swab. As mentioned previously, caution should be used whenever isolating genomic DNA to prevent shearing of the DNA. We also warm the elution buffer to increase yields. However, the problem we have with concentrating the DNA by speedvac or evaporation is that this will also concentrate the buffer. So, we use ethanol precipitation and this has worked very well for concentrating the final sample. For precipitation we use sodium acetate with 95 percent ethanol as the precipitation step. This is followed by a wash with 70 percent ethanol. The volumes used depends on what volume you are trying to purify.
Farrukh, Cynthia's suggestion really works. I recently used Oragene kit for a genotyping study from human saliva. The extraction method was similar as mentioned by Cynthia.