Marjanp145,greetings,
Drifting,in general,is often somewhat misunderstood/misinterpreted...Tool-eye in particular...I'm not sure just how well i can express this,and in any case,take it with a large grain of salt...
The support(the Bottom Tooling) is,of course,important.Normally,3-4 different sized drifts are used in forming an eye,EACH with it's corresponding bottom-tool.
However,that's not the whole story...An eye has a great Depth,as compared to a common rivet-hole,say,or other,simpler,orifice.
So just the simple force,pounding,applied to the drift soon(very)begins to work Against the process-as the friction increases,your blows are more and more becoming directed at Upsetting the sides of an eye vertically(hope that it makes sense,tough to explain in words...).They're trying to drag the material down with them,which in turn makes the orifice tighter,pressure to overcome increases,and so on...
(In the classical tradition a lubricant is always used even with the small/shallow holes,a mix of oil/charcoal dust/and such...to overcome that very effect).
In order to address these dynamics one has to continuously forge the Sides of the eye,making sure that the material is displaced in a desirable direction.Forging on the drift,of course,stretches the eye,allowing(vs forcing)the drift to do it's job(on the next heat).
This logic/technique is so effective that it actually supercedes(energy-wise)the pounding of the drift down.Sometimes,it's enough to,on a fresh heat:Insert the drift,invert it on the anvil,drift head down/forging up,and slam it pretty good,to get the drift to seat.Then forge the sides as much as possiblebefore drift loosens too much(one can be actually "air-forging" it just on the drift,with the end of drift resting on anvil/other end held in left hand/pressing the edge of forging against the anvil,to keep the drift advancing into the eye.
THEN you can go onto the bottom-tool/vice/whatever,to straighten out the newly-widened eye,vs stretching it with the drift.
Of course,one NEVER uses a machinist's vice for the make-shift bottom-tooling(or any other percussive action).Post-vice,being WI for the very purpose,does work somewhat...But only in combination,as described above....(i know it sounds obscure,sorry if it should prove to be too obscure/convoluted...)
A thick plate over tubing,with the correct orifice(-es) in it,as suggested above,would be a great asset for your shop.But even with that,don't forget that much shaping of any eye is done from the outside...Otherwise,you run the risk of setting down the locality of the eye so much,that the resulting tool will look(and haft)wrong...
O-1 is a pretty rough choice for these excercises...Naturally,"everything" is possible,but...
Personally,i've tangled with issues that confused and physically punished me to a surprising extent(in attempting to reproduce old tools,often-handled ones with an eye),and eventually i'd discover just how much difference the very material alone makes...
O-1 is an excellent alloy for the edge,and in my humble opinion,your energy would be better spent in forgewelding an inserted bit of that great alloy,into a WI or mild steel body,vs slitting and drifting an eye in it...
Once again,hope that it's all not totally confusing....The VERY best of luck with your project,