I have had many drawings enlarged this way.
I use a local company who do ordnance survey maps, so check to see if any such are available in your area.
The finished length of the drawing is no problem, as the paper comes off of a roll.
However, there is a limit on the width of the paper, which is 36 inch maximum.
As stated earlier, the enlargement factor you need, from 1/96 to 1/72, is 133%.
So, if you take your 1/96 drawing, and fold it so that it has a maximum height of 24 inches, measured from the top edge say, then you can get that section enlarged in one pass.
Then do the same measuring from the lower edge, and have that enlarged.
You should then have two sheets at 1/72 scale, one for the plan view, and the other for the side elevation.
This is assuming that both views are on one sheet of the original 1/96 drawing.
If they are on separate sheets, then fold each so that the required view is on paper no more than 24 inches wide.
Once you do this, it is then straightforward to go to printer and ask for a 133% enlargement, and you know that it will fit on the paper.
I had an Arleigh Burke drawing enlarged from 1/96 to 1/72 last week, and the cost was £20, for the two sheets, the final hull length being 84 inches.
Peter