One thing I am not clear on,was the rifle purchased with the Hart barrel,or did your dad have it put on?
In either case,the rifle is an expression of a whole process of creativity by your dad.It's not the common off-the-shelf.He had reasons why it is just the way it is.
Before you do anything I suggest you subscribe to Precision Shooting,maybe The Accurate Rifle for a year.Just read the magazines.Maybe you can read old ones online if you subscribe.Rifle might be another good mag.
With a little immersion in this material,you will be able to enter and understand what your dad was doing.You will learn the place the "triple deuce" holds with serious shooters
I strongly recommend you leave the rifle as he intended it.In time,you would regret modifying or selling it.It is "in balance" .
That twist factor previously mentioned is important.I met a guy had an XP-100 he said would not hit a mattress at 100 yds.I said I think it will shoot inside 2 in at 100.He brought it to me.He brought 55 gr whitebox 5.56 military ammo.Bullets went through the target sideways.
A .223 rechamber with 14 in twist! I loaded him some 52 gr MK's and put 10 rds in a group 1 1/4 high and 3/4 wide....at 200 yds.
All well and good,but most .223 is loaded with 55 gr or heavier bullets.Lighter bullet loads are harder to find and probably more expensive than .222.You won't get what you are trying to achieve.
Re-work:Without writing a whole lot,its easy for a smith to run the reamer in and deepen the chamber,but!!!!What is in the original chamber was done all with the .222 reamer,and a pilot riding the lands of the rifling.Likely by a highly skilled rifle maker with a new,sharp reamer.
Your smith,who is rechambering,has a .223 reamer.He has used it a number of times,and its likely a good,stock reamer from Brownells.
On a rifle like yours,critical to fine accuracy,is the leade and throat.It has to just exactly cut the lands of the rifling down to the grooves,and not a bit more.Perfectly concentric,no flaw.
Sometimes,maybe,you will get a very good job.Odds are,the leade/throat will show flaw with rework.
For now,just try.Get a set of Forster Benchrest dies,about $60.
If you want to go real cheap,get Lee's little bench press or even the little hand press outfit for $35
Get a powder scale and a couple load manual.Ask questions here.
I think you wll find you are shooting groups you can cover with a coin,very soon.Likely a dime.
I bet that rifle,as is,will shoot grapes for targets at 100 yds.With good handloads.