I'd pull the liner and plug it. It wouldn't matter if the plug was perfectly fitted to the bore on the inside.
The next step would be to deepen the existing breech plug threads to just barely past that Liner Plug just installed.
Make the new threads the same size or one step smaller if the caliber of the bbl allows.
Smaller may be easier to do for the builder.
All that needs to happen is for the new threads to completely cut through that Liner Plug coming in from the side and barely pass it by.
The face of the new breech plug will then seal off the Liner Plug and it won't be an issue as far as safety. Plus the new Flash Hole appears to be able to be placed right at the front face of that new breech plug.
The new Breech Plug,,
No need to make an entirely new Plug or modify the existing one with an extension, etc.
Take a standard thread Allan Screw of the thread that you made the extension of the breech plug threads, face it square and fit it as the new breech plug. The Allan Wrench fitting makes an easy in & out way of fitting w/no need to keep track of a tang coming up to 12 o'clock.
Once fitted, replace the orig Breech Plug into the rifle. It should turn in and come up square/12 o'clock. If the orig threads are a bit too long now and bumping against the rear of the new Allen Screw breech plug,,trim the old breech plug threads so it will turn in w/o resistance. No need for it to seat against the Allen Screw,,just for the tang section to seat firmly against the breech face and square up as originally done.
Center punch the Flash hole,,drill it.