Hi Richard,
At 300 mm depth and 20 mm dia you are in gundrilling territory – depth 15X diameter. Brochure below. No connection to firm apart from being a long term satisfied customer for their gundrills in the mould making industry.
https://www.sandvik.coromant.com/sitecollectiondocuments/downloads/global/brochures/en-gb/c-1140-543.pdf
A gundrill from these gents or from Guhring would be a top notch tool for the job but three things re DIY-
1. Gundrills are very expensive
2. your pillar drill will not likely have 300 mm depth of vertical feed, probably more like 75 mm vertical feed on many DIY pillar drills
3. your pillar drill may not have sufficient power for gundrilling
Rather than buying expensive one time use long drills or gundrills, you might consider going to a local mould making shop for injection moulds and asking them for a quote to drill your hole. Be sure to tell them it's a model engineering job and that you are not in a hurry for it. Chances are they will do a very straight, accurate hole in minimum time, since most mould shops do gundrilling every day for cooling water passages and know all the tricks. You may find the mouldmakers won't charge much to do the job if it is not a rush and you take them a tray of coffees when you pick it up.
Just food for thought. Lots of ways to get it done, as others have said.
Edited By Jeff Dayman on 09/05/2018 22:28:30