Here is my four penn'orth, for what its worth.
If space is limited, in either Horizontal or Vertical mode, 2MT Finger Collets will maximise tool/workpiece space.
To release them, you will need to bash the end of the drawbar, once it has been slackened by about half a turn.(Unless you can make up some form of "pusher" for the drawabar, to spare the spindle bearings).
Finger collets for 2MT will go upto about 12mm, but are "one size" only, whether Imperial or Metric. Trying to use for other than the stated size will damage them. An ER collet chuck will take up space, but the collets will accept upto a 1mm variation in size, so can accomodate Metric or Imperial cutters, (or work in the lathe). ER20 goes up to 13mm, ER25 to 16mm, and ER32 (probably too big for your intended use) 20mm.
They may be expensive, but grip well, and run truer than a drill chuck.
Don't use helical endmills in a drill chuck. The Drill Chuck does not have as much grip as a collet (little more than line contact vs all round in a collet), and the helix will be trying to screw the cutter out of the drill chuck. You may get lucky, but one day, the cutter WILL move out, and mess up things!
H T H
Howard