Toy Soldier boots are more or less made for a BBi foot or one that is slim and small in design. DML feet are well, big by comparison. More like the feet that was coming out with the Echo version of GIjOE.
However, there is another issue with TS boot that you need to take heed. The heel of the boot has a paper backing that quickly folds down if you force the foot of the figure into the boot. This restricts the figure's foot from going in easy and causes the figure to be off balanced when the boot is complete on. Thus causing the figure not to stand correctly. Take a little TAC-glue and glue that paper heel support to the back of the boot so it will not move. This will also make the heel portion of the boot more ridged. Let it dry before continuing. Also ensure the the laces are loose as possible without removing them.
As far as the DML foot, you don't have to cut the toes as much as make the foot a bit narrower. shaving the outside of the DML foot down a bit helps. However, you must also sand it smooth so insertion into the TS boot is unrestricted.
I am going to assume that the TS boot is made of leather/suede/cloth and therefore dry. I am also assuming it is their Jungle boot or their very early desert boot. Adding a little olive oil to the DML foot helps make it slide in a little easier but you still will have to work at it.
Slide the figures foot in but push from the heel of the foot will pulling up on the back portion of the boot. Make sure the foot does not get caught on any material in side the boot as you are working it in. This will still take effort and you will have to be patient and just work at it.