diet hasnt been mentioned that much on here, whether you do interval training or standard running it matters little if your eating massive amounts of food or even worse massive amounts of the wrong food.
and someone who has a lot of weight to loose in 6 weeks (like 13kg!!!) will most definitely need to be on a completely different training programme/diet.

if you put that much weight on in between fights then you are giving yourself a mountain to climb every time fight training starts.

starting fight training/correct diet the appropriate time before a fight is important (assuming that people dont eat well in between fights). some people think 8 weeks is too long before but it allows you to split the training up into stages with the first part focusing more on the bulk of the weight coming off (if needs be) then increasing the intensity of the work and loosing the remaining weight steadily and safely as the weeks go on.

imo weight cutting shortly before the fight is dangerous and messing with your body on a cellular level. if you cant make a weight or at least 1 or 2kg near it in time for a fight then you shouldnt be fighting at that weight. thats only my opinion however, i know other people disagree especially in the case of high level pro fighters.

as far as running v interval training is concerned they both have their place in prep. again just our way of doing things, but our fighters do 3 long runs a week if they have some weight to shift in the first part of training and one set of intervals at the local track, in stage 2 (4 weeks out) they change to hill sprints 3 times a week and one set of flat intervals. obviously combined with everything else. it works fine for them. but every fighter/body is different. trial and error!