Gus, I think that the boring problems which you are experiencing is all too common on on 'light lathes' and really farting about with most reamers is on a hiding to nothing. OK, I have reamers and the facility to sharpen them and whatever but most are tapered and, I'm sure that no one wants a tapered bore?
Again, you can get a scrap Allen key or even a broken drill or even a Bicycle spoke and broken centre drills but the odds are that - well,, you know!
The only way to achieve 100% 'perfection is to bore between centres. It doesn't matter a hoot if your tailstock is 'out' by a thous or a week, but the bore will be round and parallel. Indeed, if you ever get around to making a Quorn you need to bore TWO holes in two castings- dead in line and three a dead inch and the fourth an inch plus 3 thous.
I did mine on a somewhat rickety old Myford and none of this milling machine nonsense. I hadn't a mill and I simply could not afford to buy one. I finally made a Ned Westbury from home made castings full of holes!
So back to boring bars, well I made TWO because the Quorn needs another bigger hole and I used the George Thomas design in his Model Engineers Workshop Manual. GHT also debunks reamers and describes making ordinary conventional boring tools and those for screwcutting.
Frankly, you follow him and succeed.
I followed GHT and Martin Cleeve and added Tom Walshaw as Tubal Cain and Dennis Chaddock. All were tool makers of exhibition standard both full size and in models. I simply mumble my appreciation.
Let me know how you get on
Norman