Hello Sanddan:
Yes, deep holes are kind of a pain on a manual machine. But as Mr. Dawson suggests, they are certainly doable. Your Length to Diameter ratio (L/D) is 32:1. First of all, take a look at the manufacturers surface speed and feed rate recommendations. Speeds for plain carbon steels 180-280 BHN hardness (1008, 1010, 1018, 1020, 1026, 1040, 1045, etc.) range from 45 to 70 surface feet per minute (SFM) on Carbide Depot's website for High Speed Steel (HSS) with a 118 deg. point. We do a little math and find the lowest speed in the range in RPMs equals .125 x 3.14 divided by 12" = .0327 ft. per revolution. To achieve 45 SFM, divide 45 SFM by .0327 and choose the RPM that most closely matches the recommendation. 45/.0327 = 1,376 RPM. Since you will be hand feeding it with your tail stock, you will have to go with "feel". I always use a drop or two of Tap Magic on the drill point to reduce galling and adhesion, but most any manufacturers cutting fluid will help. Always use a center drill, as you did, on shallow and deep holes. Starting with a shorter drill is always a smart move but make sure that the drill has an accurate grind for those that regrind your own drills. And with a manual machine, peck often, and you will get the feel of how often to retract. If you feel any rumbling, retract, re-lube, do it again.
Good luck!
Best Regards, Gary