It takes work to get a rifle to shoot well, doesn't matter if it is a bolt gun or a Handi, but the Handi has it's own set of problems that need to be addressed and solved BEFORE it will shoot it's best.
Here is my latest daymare...another switch barrel. 222 Rem Mag. Originally it was a Ruger MKII 223 All Weather with a light #1 contour barrel, but I couldn't get it to shoot worth a hoot. I pulled the barrel and used the action for another of my wild hairs.
I cut off the Ruger threads and 1/2" of muzzle, threaded it 20TPI to fit this stub receiver and used a 60° center to cut the crown about 1/4" deep, a year or so ago and just rechambered it to 222 RM a couple weeks ago. I also made a forend out of aluminum and full bedded it. I cut two dovetails in the thick part of the barrel at the chamber end and installed two T/C 10-32 forend mounts.
The stub receiver is steel epoxy bedded to the frame also.
As far the ammo is concerned the brass is R-P 222 RM with an amazing weight uniformity...normally this doesn't happen with R-P...I weighed out 50 and the range was 215 to 218 gr with most hitting 217 gr. I was going to go with Lapua if the rig proved capable and it did, but I will stick with the R-P I think and save my money.
The bullets are 35gr Hornady VMax's seated to 2.18" OAL with them touching the lands at 2.19". The Hornadys were also very uniform as to ogive length, weight and OAL.
The rifle and groups. The groups were shot as the rifle sits..off the bipod with a sandbag under the butt.
I started with a load near the top of the range and 2.16" OAL, 3 round groups. The first 3 were perfectly in line vertically...I started reducing by .3 gr and the verticals got closer until I got a nice triangle, then the groups went horizontal. This was a classic load development.
I went back to where the group was triangle with the load and started increasing the OAL length in 0.005" increments. Again a classic behaviour...the load kept getting smaller and smaller. I will increase the powder by another .3 and see how the velocity and group acts, but for all intents and purposes I will load up 50 with this load and go hunting before the winter sets in
I've done this type of load development with all my rifles and pistols...Been doing the same thing for half a century. I've taken rifles that "don't shoot for krap" and turned them into half-inchers many times...but I have to say that the Handi is one of the hardest shooters to get straightened out of all the cannons I have played with.
The difference between the left and right group is the left group is 2.18" OAL and the right group is 2.175"...0.005" difference in length. This normally doesn't happen except in benchrest quality barrels.
The 2.18" load chronoed ~3600fs using RL10X.
Heating can cause groups to walk every whichaway, but depending on what your accuracy expectations are and what level of prepping you do, a rifle can shoot well or very poorly. This is a system, a complicated system and you have to address ALL the different parameters if you want it to shoot well.
Luck