Single shot Handi Rifles have their quirks but most of them are really good shooters but you have to do your part as well.
Most of the accuracy problems with the .243 come from not letting the barrel cool between shots, and the forend.
You are on the right track by removing the forend and where you rest the rifle is important for consistent shooting. Placing the rest just behind the hindge pin, and foreward of the trigger guard is recommended.
More detail on accurizing can be found in the FAQ's at the top of the page. It goes into detail about using an "O" ring on the take down screw, and maybe even bedding the forend.
Stay away from oil on the latch shelf as Handi Rifles don't like a lot of oil.
Lighter bullets seems to shoot well, but others have had luck with 100 grain loads as well, and finding the right combination is half the fun.
Good luck, and others will chime in I'm sure!